Sour Gas Sweetening and Ethane/Ethylene Separation

Sour Gas Sweetening and Ethane/Ethylene Separation

A DISSERTATION

SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL

OF THE UNIVERSITY OF MINNESOTA

BY

Mansi S. Shah

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

J. Ilja Siepmann and Michael Tsapatsis

May, 2018

c© Mansi S. Shah 2018ALL RIGHTS RESERVED

Acknowledgements

It is globally recognized that the Chemical Engineering program at University of Min-

nesota is one of the most scholarly programs and I am sincerely indebted for the oppor-

tunity to spend foundational years of my research career in this department. I have had

a truly wonderful five and a half years here and would like to thank several people for

their unflagging support all through these years.

I thank both my Ph.D. advisors, Prof. J. Ilja Siepmann and Prof. Michael Tsapatsis,

for their strong support and guidance. Constant interactions with Professor Siepmann

has greatly enriched my understanding of chemical phenomena. His patience and en-

couragement under difficult times in greatly acknowledged. I thank Professor Tsapatsis

for his critical insights on several subjects of research that I have had the privilege to

interact with and learn from him. I would like to also acknowledge the opportunity to

serve as the laboratory safety officer for his group for two and a half years. I am very

grateful for the opportunity to carry out research in both theses groups and acquire

a unique combination of skills in molecular simulations and experiments. While every

detail of science and engineering that I have learnt from these two professors is truly

amazing, I am most grateful to them for training me in becoming a better researcher

and making me equipped with the right attitude and passion to pursue a lifelong career

in science and engineering.

I thank all my committee members for their valuable insights on my thesis. I would

like to thank our graduate program coordinator, Julie Prince, for the immense amount of

work that she puts in so that all the graduate students, and especially the international

students, can have an effortless and enjoyable stay in the department. I acknowledge

the Chemical Engineering & Materials Science department and the graduate school for

the graduate studies and doctoral dissertation fellowships and also the US Department

i

of Energy for research funding.

Furthermore, I would like to acknowledge my colleagues and friends in both research

groups, especially Swagata Pahari, Evgenii Fetisov, Peng Bai, Rebecca Lindsey, Balasub-

ramanian Vaithilingam, Meera Shete, and Dandan Xu for an exciting and collaborative

graduate experience. I would also like to thank my friend and fellow graduate student,

Akash Arora, for our intense discussions on science and engineering and for his invaluable

support and understanding.

Finally, I would like to thank my parents, Sanjeev Shah and Alka Shah, for their

unwavering support, blessings, and sacrifices. And last but certainly not the least, I

would like to thank my sister, Dishita Shah, for the strong encouragement and emotional

support that she has always been.

ii

Dedication

To my parents

iii

Abstract

Chemical separations are responsible for nearly half of the US industrial energyconsumption. The next generation of separation processes will rely on smart materialsto greatly relieve this energy expense. This thesis research focuses on two very energy-intensive and large-scale industrial separations: sour gas sweetening and ethane/ethyleneseparation.

Traditionally, gas sweetening has been achieved through amine-based absorption pro-cesses to selectively remove H2S and CO2 from CH4. Ethane/ethylene is an even hardermixture since the two molecules have very similar sizes, shapes, and self-interactionstrengths. Despite their low relative volatility (1.2–3.0), cryogenic distillation is themost commonly used technique for this separation. Compared to absorption and cryo-genic distillation, adsorption allows for better performance control by choosing the rightadsorbent. Crystalline materials such as zeolites, that have precisely defined pore struc-ture, exhibit excellent molecular sieving properties. Performance is closely linked tostructure; identifying top zeolites from a large pool of available structures (∼ 300) isthus crucial for improving the separation. In this thesis research, molecular modeling isused to identify optimal materials for these two separations.

Since the accuracy of predictive molecular simulations is governed by the underlyingmolecular models, the first objective of this thesis research was to develop improvedmolecular models for H2S, ethane, and ethylene. A wide variety of properties suchas vapor–liquid and solid–vapor equilibria, critical and triple points, vapor pressures,mixture properties, relative permittivities, liquid structure, and diffusion coefficientswere studied using molecular simulations to parameterize transferable molecular modelsfor these molecules. These models are designed to strike a very good balance betweenaccuracy of predictions and efficiency of simulations. For some of the zeolites for whichexperimental data existed in the literature, purely predictive adsorption isotherms agreedquantitatively with the available experiments. A computational screening was thenperformed for over 300 zeolite structures using tailored molecular simulation protocolsand high-performance supercomputers. Optimal zeolites for each of the two applicationswere identified for a wide range of temperatures, pressures, and mixture compositions.

Finally, a brief literature survey of the zeolites that have been synthesized in their

all-silica form is presented and syntheses for two of the important target framework types

is discussed.

iv

Contents

Acknowledgements i

Dedication iii

Abstract iv

List of Tables viii

List of Figures ix

1 Introduction 1

1.1 Sour Gas Sweetening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Ethane/Ethylene Separation . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Adsorptive Separations Using Zeolites . . . . . . . . . . . . . . . . . . . 5

1.4 Molecular Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Development of the Transferable Potentials for Phase Equilibria Model

for Hydrogen Sulfide 10

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2 Force Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.1 Model Development . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.2 Methane and Carbon Dioxide . . . . . . . . . . . . . . . . . . . . 16

2.3 Simulation Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

v

2.4.1 Liquid-Phase Relative Permittivity . . . . . . . . . . . . . . . . . 19

2.4.2 Unary Vapor–Liquid Equilibria . . . . . . . . . . . . . . . . . . . 20

2.4.3 Binary Mixture with Carbon Dioxide . . . . . . . . . . . . . . . . 24

2.4.4 Binary Mixture with Methane . . . . . . . . . . . . . . . . . . . . 29

2.4.5 Ternary Mixture with Methane and Carbon dioxide . . . . . . . . 31

2.4.6 Liquid-Phase Radial Distribution Functions . . . . . . . . . . . . 31

2.4.7 Liquid-Phase Self-Diffusion Coefficient . . . . . . . . . . . . . . . 32

2.4.8 Solid-Phase Structure and Relative Permittivity . . . . . . . . . . 33

2.4.9 Triple Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3 Monte Carlo Simulations Probing the Adsorptive Separation of Hy-

drogen Sulfide/Methane Mixtures Using All-Silica Zeolites 39

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39


3.2.1 Molecular Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

3.2.2 Simulation Details . . . . . . . . . . . . . . . . . . . . . . . . . . 41


3.3.1 Unary Adsorption . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.3.2 Binary Adsorption of H2S/CH4 Mixtures . . . . . . . . . . . . . . 46

3.3.3 Assessment of Ideal Adsorbed Solution Theory . . . . . . . . . . 56

3.3.4 Binary Adsorption of H2S/H2O Mixtures . . . . . . . . . . . . . 60

3.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

4 Identifying Optimal Zeolitic Sorbents for Sweetening of Highly Sour

Natural Gas 63

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63


4.2.1 Molecular Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.2.2 Simulation Details . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.2.3 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67


4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

vi

5 Transferable Potentials for Phase Equilibria. Improved United-Atom

Description of Ethane and Ethylene 74

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74



5.3.1 Unary ethane VLE . . . . . . . . . . . . . . . . . . . . . . . . . . 80

5.3.2 Unary ethylene VLE . . . . . . . . . . . . . . . . . . . . . . . . . 85

5.3.3 Binary ethane/ethylene VLE . . . . . . . . . . . . . . . . . . . . 88

5.3.4 Binary ethylene/CO2 VLE . . . . . . . . . . . . . . . . . . . . . . 94

5.3.5 Binary ethane/CO2 VLE . . . . . . . . . . . . . . . . . . . . . . 96

5.3.6 Binary H2O/ethane VLE . . . . . . . . . . . . . . . . . . . . . . 97

5.3.7 Binary H2O/ethylene VLE . . . . . . . . . . . . . . . . . . . . . 99

5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6 C2 Adsorption in Zeolites: In Silico Screening and Sensitivity to Molec-

ular Models 103

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

6.2 Simulation Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104


6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

7 Zeolite Synthesis: Literature Survey and Potential Future Targets 116

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

7.2 All-Silica Zeolites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

7.3 Low-Polarity Zeolite Synthesis Targets . . . . . . . . . . . . . . . . . . . 120

7.3.1 Framework Type DFT . . . . . . . . . . . . . . . . . . . . . . . . 120

7.3.2 Framework Type AWO . . . . . . . . . . . . . . . . . . . . . . . 122

8 Conclusions 124

References 127

vii

List of Tables

2.1 Bond lengths and bond angles for TraPPE models . . . . . . . . . . . . 13

2.2 Force field parameters: partial charges (qi), LJ parameters (εii and σii),

and displacement (δS−X) of off-atom X site. . . . . . . . . . . . . . . . . 14

2.3 Dipole moment, liquid-phase density, and relative permittivity at 194.6 K

and 1 atm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.4 Normal boiling point, critical properties, and accentric factor for hydrogen

sulfide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.5 Liquid-phase density, calculated self-diffusion coefficient for a 1000-particle

system, and extrapolated bulk-limit self-diffusion coefficient at 206.5 K

and 1 atm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.1 Zeolite unit cell parameters and simulation box sizes. . . . . . . . . . . . 42

3.2 Calculated Henry’s constants for hydrogen sulfide and methane in all-

silica zeolites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.3 Compositions and selectivities for vapor–liquid and adsorption equilibria

in MFI calculated for the binary H2S/H2O mixture at T = 298 K and

p = 1 bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.1 Force field parameters: geometry, LJ parameters, and partial charges. . . 77

5.2 Normal boiling point, critical properties, and acentric factors for ethane. 83

5.3 Optimized parameters for different ethylene models. . . . . . . . . . . . 85

5.4 Normal boiling point, critical properties, and acentric factors for ethylene. 86

7.1 Framework types with all-silica synthesis (largest ring being eight- or nine-

membered). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

7.2 Framework types with all-silica synthesis (ten-membered rings or larger). 119

viii

List of Figures

1.1 Block diagram for natural gas processing. . . . . . . . . . . . . . . . . . 3

1.2 Block diagram for manufacturing ethylene. . . . . . . . . . . . . . . . . . 4

1.3 Schematic representation of the canonical (NV T ) Gibbs ensemble. . . . 7

2.1 Schematic representation of the types of H2S models. . . . . . . . . . . . 14

2.2 Vapor–liquid coexistence curves for hydrogen sulfide. . . . . . . . . . . . 21

2.3 Saturated vapor pressure versus inverse temperature for H2S. . . . . . . 22

2.4 Relative deviations in liquid density and saturated vapor pressure of H2S

as a function of temperature. . . . . . . . . . . . . . . . . . . . . . . . . 24

2.5 Pressure–composition diagram and separation factor for the H2S/CO2

mixture at T = 293.16 K. . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.6 Pressure–composition diagram and separation factor for the H2S/CO2

mixture at T = 333.16 K. . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.7 H2S–CO2 radial distribution function and number integrals. . . . . . . . 28

2.8 Pressure–composition diagram and separation factor for the H2S/CH4

mixture at T = 277.60 and 310.94 K. . . . . . . . . . . . . . . . . . . . . 30

2.9 Ternary phase diagram of CH4/CO2/H2S system at T = 238.76 K and

p = 34.47 bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.10 Intermolecular radial distribution functions for liquid H2S. . . . . . . . . 33

2.11 Clausius–Clapeyron plot near the triple point. . . . . . . . . . . . . . . . 35

2.12 Snapshots of the final configuration from slab simulations. . . . . . . . . 36

2.13 Temperature dependence of the slab-averaged order parameter. . . . . . 37

3.1 Unary adsorption isotherms for H2S and CH4 in all-silica zeolites. . . . . 44

3.2 H2S versus CH4 selectivity as a function of vapor-phase composition. . . 46

3.3 H2S versus CH4 selectivity as a function of H2S loading. . . . . . . . . . 48

ix

3.4 Spatial distribution of adsorption in MFI and MOR zeolites. . . . . . . . 49

3.5 Partial molar enthalpies of adsorption from binary simulations. . . . . . 52

3.6 Dependence of selectivity (logarithmic) on differential adsorption enthalpy. 53

3.7 Comparison of H2S aggregation in the zeolite and gas phases. . . . . . . 54

3.8 Dependence of selectivity on differential adsorption enthalpy for different

zeolites at T = 298 K and p = 1 bar. . . . . . . . . . . . . . . . . . . . . 55

3.9 Comparison of H2S and CH4 loadings from binary simulations and pre-

dicted using ideal adsorbed solution theory (IAST). . . . . . . . . . . . . 57

3.10 Ratio of loadings predicted using IAST and obtained directly from simu-

lations for binary mixtures as a function of simulated H2S loading. . . . 58

3.11 Ratio of adsorption selectivities predicted using IAST and obtained di-

rectly from binary simulations. . . . . . . . . . . . . . . . . . . . . . . . 59

4.1 Binary H2S/CH4 and H2S/C2H6 adsorption at different feed concentra-

tions of H2S: yF = 0.50, 0.30, and 0.10 at T = 343 K and p = 50 bar. . . 69

4.2 Selectivities and adsorption enthalpies for top-performing zeolite structures. 70

4.3 Five-component (H2S/CO2/CH4/C2H6/N2) sour gas adsorption in zeolites. 72

5.1 Schematic drawings of ethane and ethylene models. . . . . . . . . . . . . 77

5.2 Vapor–liquid co-existence curves for ethane. . . . . . . . . . . . . . . . . 80

5.3 Clausius-Clapeyron plot for ethane. . . . . . . . . . . . . . . . . . . . . . 81

5.4 Percentage errors with respect to the experimental measurements in vapor

pressure, vapor density, and liquid density versus temperature for different

ethane models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.5 Percentage errors with respect to the experimental measurements in vapor

pressure, vapor density, and liquid density versus temperature for different

ethylene models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

5.6 Vapor–liquid co-existence curves for ethylene. . . . . . . . . . . . . . . . 88

5.7 Clausius-Clapeyron plot for ethylene. . . . . . . . . . . . . . . . . . . . . 89

5.8 Binary ethane–ethylene phase behavior at T = 263.15 K. . . . . . . . . . 91

5.9 Binary ethane–ethylene phase behavior at T = 161.39 K. . . . . . . . . . 92

5.10 Binary ethane–ethylene phase behavior at constant pressure. . . . . . . . 93

5.11 Binary CO2–ethylene phase behavior at T = 263.15 K. . . . . . . . . . . 94

5.12 Effect of combining rules on the binary CO2–ethylene phase behavior. . 95

x

5.13 Binary CO2–ethane phase behavior at T = 263.15 K. . . . . . . . . . . . 97

5.14 Solubility of ethane in water versus pressure at T = 444.26 K. . . . . . . 98

5.15 Solubility of ethylene in water versus pressure at T = 411 K. . . . . . . . 99

5.16 Energetics for the H2O–ethylene dimer. . . . . . . . . . . . . . . . . . . 100

6.1 Unary adsorption isotherms of C2H6 and C2H4 in MFI zeolite. . . . . . 107

6.2 Performance of zeolitic frameworks from the IZA–SC database for the

separation of a 50:50 binary mixture of ethane and ethylene at T = 300 K

and p = 20 bar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

6.3 Unary adsorption isotherms of C2H6 and C2H4 in DFT zeolite. . . . . . 110

6.4 Potentials of mean force for ethane and ethylene in ACO, DFT, and UEI

zeolites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

6.5 Unary adsorption isotherms of C2H6 and C2H4 in ITW zeolite. . . . . . 113

6.6 Unary adsorption isotherms of C2H6 and C2H4 in RRO zeolite. . . . . . 114

xi

Chapter 1

Introduction

Precise purity of a chemical or a composition of a mixture of chemicals is one of the key

attributes that determines the utility and value of a feedstock for a variety of applica-

tions. Chemicals separation to attain the desired purity forms an integral part of the oil,

gas, and chemicals industries and is responsible for nearly half of the US industrial energy

consumption. [1] Separation of the different boiling fractions of crude oil, olefin/paraffin

separation, separation of xylene isomers, air separation, and alcohol/water separation

constitute just a few examples from the long list of separation challenges faced by these

industries. It is interesting that although significant amount of research and develop-

ment in separation technology has already taken place over the last century, the need

for more efficient processes continues to inspire new research in this field.

The phenomena of mixing of two or more compounds results in an increase in the

entropy of the system, which in turn results in a decrease in its free energy. This is the

underlying reason as to why work needs to be done in order to separate the components

of a mixture. Since work is not a state function, it depends on the path or the process

that one chooses for the separation. And it may be appropriate to infer that it is the

effort to enhance the extent of reversibility of the process, that has continued to sustain

separations research for several decades. In this Ph.D. thesis, the focus is on two of the

very energy-intensive and high-throughput industrial separations: sour gas sweetening

and ethane/ethylene separation.

1

Chapter 1: Introduction 2

1.1 Sour Gas Sweetening

Today and in the near future, fossil fuels remain the single largest contributors to world

energy requirements. While developing renewable energy resources is part of the answer

for mitigating climate change, using natural gas instead of coal results in significant

reduction of CO2 emissions. In 2016, natural gas constituted 29% of the US energy

mix. [2] Ever since the first gas well was drilled about 200 years ago, natural gas continues

to find use in a multitude of applications ranging from fuel for cooking, lighting, heating,

and automobiles, to a chemical feedstock for a wide array of chemical industries.

Raw natural gas is a complex mixture comprising of mainly methane (CH4), but also

ethane and other light alkanes, hydrogen sulfide (H2S), carbon dioxide (CO2), nitrogen

(N2), and water (H2O) vapor. H2S is a very toxic gas; it causes irritation to eyes, nose,

and throat at concentrations as low as 10 ppm, and results in an almost instant death at

concentrations above 1000 ppm. The Environmental Protection Agency classifies natural

gas as sour at H2S concentrations above 4 ppm. Large gas reserves are untapped today

due to the difficulty involved in processing low-quality sour gas. Sweetening of natural

gas refers to removal of acidic sulfur compounds, primarily H2S.

Natural gas emerging at the reservoir well head is subjected to low temperatures to

condense out heavier hydrocarbons, while vapors are sent to the Acid Gas Removal Unit

(AGRU) to selectively strip off H2S and CO2, typically using a highly energy-intensive

amine-based absorption process (see Figure 1.1). Overhead vapors are sent to the acid

gas removal unit to selectively strip off H2S and CO2; amine-based absorption is most

commonly used for this step. The H2S-rich stream is sent to the sulfur recovery unit

(SRU), while the CH4-rich stream, after some post-processing steps such as dehydration,

is sent to the pipeline as sales gas. In the SRU, sulfur is recovered by the well-known

Claus process, where H2S undergoes high-temperature (≈ 1000 ◦C) thermal oxidation:

H2S + 1.5O2 → SO2 + H2O −∆H = 518 to 576 kJ/mol of H2S, [3] (1.1)

prior to low-temperature (200–300 ◦C) catalytic oxidation:

2H2S + SO2 ↔ 3S + 2H2O −∆H = 88 to 146 kJ/mol of SO2, [3] (1.2)


Figure 1.1: Block diagram for natural gas processing. Reprinted with permissionfrom M. S. Shah, M. Tsapatsis, and J. I. Siepmann, Chem. Rev. 2017, 117, 9755–9803. Copyright 2017 American Chemical Society. https://pubs.acs.org/doi/abs/10.1021/acs.chemrev.7b00095

in a series of reactors at progressively lower temperatures, and accompanied with sulfur

removal in intermediate condensers. Since the melting point of elemental sulfur is 115 ◦C

and sulfur deposition leads to catalyst deactivation, the temperature of the final Claus

reactor is generally maintained above 200 ◦C. This results in an incomplete conversion

of H2S and the resulting gas stream is sent to the tail gas treatment unit for additional

sulfur recovery before releasing the waste gases to the atmosphere. Thus, highly sour

natural gas is usually processed for H2S removal in two different units, at two very

different concentrations.

The high H2S content of newer gas fields and increasingly stringent government

regulations on permissible sulfur emissions will soon render the existing H2S clean-up

technology economically unfeasible. Thus, as demands for cleaner energy resources con-

tinue to rise and also as we start exploring the more difficult, i.e., sourer, gas wells,

better H2S removal technologies will become pivotal.

https://pubs.acs.org/doi/abs/10.1021/acs.chemrev.7b00095

https://pubs.acs.org/doi/abs/10.1021/acs.chemrev.7b00095


Figure 1.2: Block diagram for manufacturing ethylene.

1.2 Ethane/Ethylene Separation

With a global capacity of about 150 million tons per annum, [4] ethylene is one of the

most important building blocks for the chemical industry. In the US alone, capac-

ity expansions at existing facilities and addition of six new crackers, are expected to

increase the domestic C2H4 production by 40%. [4] Ethylene is manufactured by high-

temperature cracking of feedstocks such as naphtha and ethane, followed by extensive

low-temperature separations to achieve polymer-grade (99.95%) purity (see Figure 1.2).

Only about 20% of the energy consumption is used for the cracker reactions, the re-

mainder 80% is consumed in the separation train. [5] Chemical separations account for

about 10–15% of the US total energy consumption; purification of C2H4 and propylene

alone accounts for 0.3% of the current global energy use. [1] With the growing market for

C2H4, more energy-efficient C2 separations become even more important.

The value of relative volatility for the C2H4/C2H6 mixture varies between 1.5 to

3.0 depending on the temperature and composition. Even with values being so close

to unity, deeming distillation as an energy and capital intensive separation method, it

has been the preferred unit operation ever since. In the last 40 years or so, there have

been consistent research efforts to develop alternative solutions such as membranes [6–8]

and adsorbents [9–23] for separating C2H6 and C2H4. While membranes may be the

ultimate answer to achieve energy efficiency for most chemical separations, commercial

deployment of membrane technology suffers from several limitations such as narrow range

of operation conditions, high costs, short lifetimes, etc. [6,24] In the interim, developing


the right adsorbent material, that offers high selectivity and working capacity, low heat

of adsorption, and easy regeneration, can contribute immensely towards saving energy

and reducing carbon emissions.

1.3 Adsorptive Separations Using Zeolites

Adsorption is a surface phenomena in which atoms, molecules, or ions can be attracted

to a surface by virtue of its high energy. And by the differential strength of interaction

of the surface with different species in the mixture, it is easy to envision the separation

of a mixture into its components. Molecular sieves are a special class of adsorbents with

pore diameters of the order of molecular dimensions and these adsorbents can also allow

for the size-based separation instead of the conventional affinity-based separation.

Over the years, nanoporous materials such as zeolites and metal–organic frameworks

have demonstrated their potential as selective adsorbents for separations and are cur-

rently used in numerous commercial processes like the production of oxygen enriched air.

The stability of zeolites under harsh chemical and thermal environments and a precisely

defined pore structure make them strong candidates for various commercial applica-

tions. Structurally, zeolites are crystalline porous aluminosilicates, which are based on a

three-dimensional network of silica and alumina. Their pores are defined by their crystal

structure and have precise sizes and shapes, allowing them excellent sieving properties

at a molecular level. The database of the Structure Commission of the International

Zeolite Association, IZA–SC, [25] reports 235 different zeolite topologies. Performance is

linked to structure; identifying the best-performing zeolite from a large pool of available

structures is thus crucial to developing a new separation technology.

As described earlier, H2S is a highly toxic gas, and performing a wide experimental

screening of all zeolites will not only be a very expensive endeavor, but will also require

stringent safety measures. This is an apt situation for molecular modeling (computer

experiments) to take the lead and guide real experiments. Computational discovery of

optimal materials for separations has not only accelerated materials screening, but is

also providing molecular insights, thus aiding design of new materials. [23,26–30] Realistic

computer modeling of observable and/or hypothesized phenomena is conceivable today;

thanks to advancements in computational algorithms [31–33] and development of accurate


molecular models. [34–37]

1.4 Molecular Simulations

Statistical thermodynamics provides a framework to relate macroscopic observable prop-

erties of a system to the microscopic atomic or molecular-level details. Some problems

are completely solvable, for example, the ideal gas law (pV = NkBT ) can be fully

derived from statistical arguments. However, as the system density increases and as

particles begin to interact, the partition function quickly increases in complexity. Until

the advent of molecular simulations, scientists were restricted to study only a very small

fraction of real world problems from a microscopic viewpoint. Use of molecular simu-

lations has enabled computation of a variety of complex phenomena such as phase and

sorption equilibria, thermophysical properties of compounds, interfacial properties, and

transport barriers.

Molecular dynamics (MD) [38] and Monte Carlo (MC) [39] are the two broad categories

for particle-based molecular simulations. Each of these methods generate trajectories in

phase space. Properties of interest are computed at these microstates and are averaged

to obtain macroscopic properties of the system. In an MD simulation, natural time

evolution of Newton’s classical equations of motion is used to sample configurations.

Particles follow a deterministic trajectory in a 6N -dimensional phase space (3N posi-

tions and 3N momenta for an N particle system). In this method, a macroscopically

observable thermodynamic property M is calculated as a time-averaged property:

M = 〈M〉time = limτ→∞

1

τ

∫ τ

0M(τ)dτ . (1.3)

Unlike MD, which is intuitively simple to imagine, Monte Carlo involves generation of

a series of configurations (Markov chain) by employing random moves. These configu-

rations are either accepted or rejected in accordance with the acceptance rule for the

attempted move. Since MC attempts a random move for each step, it is stochastic in na-

ture. Here the momentum integral over the 3N momenta is factored out and we need to

sample only in the 3N -dimensional co-ordinate space, making MC less memory-intensive

compared to MD. There is no notion of time, and macroscopic properties are computed


Phase APhase B

ΔV− ΔV

ΔN

Figure 1.3: Schematic representation of the canonical (NV T ) Gibbs ensemble.

as an ensemble-average over configurations of a simulation:

M = 〈M〉ensemble = limNstep→∞

1

Nstep

Nstep∑i=0

M(i) . (1.4)

While both MC and MD can be used to compute equilibrium properties, MC methods

cannot be used to compute dynamical properties. Compared to MD, MC can be highly

computationally efficient, because by attempting a variety of moves, one is not limited

by slow events such as overcoming an activation barrier.

A collection of systems, each with a fixed value for certain macroscopic variables,

forms a statistical mechanical ensemble, and these variables define the type of the en-

semble. For example, a system with N particles, enclosed in a volume V , and at a

temperature T , can have several microstates (different positions and momenta of the N

particles). Each of these microstates together constitute the NV T or canonical ensem-

ble, where N , V , and T , are macroscopic variables characterizing the ensemble. There

are many other ensembles such as, microcanonical (NV E), grand canonical (µV T ),

isothermal-isobaric (NpT ), and the Gibbs ensemble. Each ensemble has its own par-

tition function, and a limiting distribution. The challenge is to find this distribution.

In the thermodynamic limit (N → ∞), relative fluctuations in the system → 0, all

ensembles become equivalent, and system attains one observable value for each thermo-

dynamic state variable. So in principle, one could use any ensemble. However in real

life, one is limited by the size of the system that can be simulated and also the length

of the simulation. Therefore, one also needs to consider the efficiency of sampling while


choosing an ensemble for simulation. In addition, there are some physical and compu-

tational advantages of a certain ensemble, in a certain situation. For instance, when

simulating vapor–liquid equilibria (VLE) for a system, the Gibbs ensemble, [31,40] which

uses thermodynamically interacting, but separate vapor and liquid boxes without an

explicit interface, is preferable over a single box canonical ensemble. This is because sta-

tistical uncertainties in simulating an interface with an affordable system size are large.

The Gibbs ensemble does not require specification of the chemical potential (µ), unlike

grand canonical ensemble, where µ is input from experimental equations of state. Differ-

ent MC moves are attempted to sample the phase space (see Figure 1.3). Translations

and rotations of molecules allow to sample the thermal degrees of freedom and attain the

criteria of temperature equality for the two phases. Volume exchanges between the two

boxes ensures mechanical equilibrium, or pressure equality, for the two phases. Finally,

particle swaps between the two boxes ensures that the chemical potential of each species

in the two co-existing phases is equal.

1.5 Thesis Outline

This thesis is an effort towards exploring the potential of zeolitic adsorbents for two

key separation applications: sour gas sweetening and ethane/ethylene separation. The

main contributions of this work are identifying potential zeolite structures for each of

these two applications and the development of accurate and efficient molecular models

for hydrogen sulfide, ethane, and ethylene.

Since the accuracy of predictive modeling is heavily contingent on the accuracy of

inputs to simulations, much effort was invested in developing a new theoretical model

to accurately describe H2S. The pure-component and binary vapor–liquid equilibria

with CH4 and CO2, the relative permittivity, the triple point, and transport properties

were used to realize a four-site H2S model. This representation of H2S is not only more

accurate than any other model in the literature, but is also a very computationally

efficient model. The results from this study, which provide a robust H2S model that can

be used for simulating diverse systems containing H2S, are described in Chapter 2.

The newly developed model was used to investigate adsorption of H2S in select zeolite


frameworks. Binary mixture adsorption of H2S and CH4 was studied at varying compo-

sitions, pressures, and temperatures to understand adsorption at a molecular scale. The

applicability of ideal adsorbed solution theory to our systems of interest was investigated.

Most natural gas wells contain H2O as an additional impurity and H2O, with its higher

electrostatic interaction strength, possesses a higher affinity for strong adsorption sites,

thus making it difficult to find a material that will adsorb H2S in preference to H2O. The

objective of this work was to test the hypothesis that the hydrophobicity of all-silica zeo-

lites [41] may be exploited to selectively capture H2S from moist natural gas. The results

from this study, which establish the potential use of zeolites for natural gas sweetening,

are described in Chapter 3. A computational screening was then performed for hundreds

of zeolite structures available from the IZA–SC database to identify the best-performing

zeolite structures for various natural gas compositions. Multi-component mixture calcu-

lations are performed for the most promising structures to quantify performance under

actual reservoir conditions. The results from this study, which identify optimal zeolites

for sweetening of highly sour natural gas mixtures, are described in Chapter 4.

Since the differences between ethane and ethylene are quite subtle, very accurate force

fields are desired to reliably screen materials for their separation. Chapter 5 contains the

development of a more accurate and efficient version of the united-atom version of the

transferable potentials for phase equilibria (TraPPE–UA2) force fields for ethane and

ethylene. Chapter 6 contains a screening study of all the zeolite structures for adsorptive

separation of ethane and ethylene.

Chapter 7 briefly reviews the literature on synthesis of pure-silica zeolites and presents

a literature review and possible future synthesis directions for two of the framework types

in their low-polarity forms for application in sour gas sweetening and ethane/ethylene

separation.

Chapter 2

Development of the Transferable

Potentials for Phase Equilibria

Model for Hydrogen Sulfide

Reprinted with permission from M. S. Shah, M. Tsapatsis, and J. I. Siepmann, J. Phys.

Chem. B 2015, 119, 7041–7052. Copyright 2015 American Chemical Society. https:

//pubs.acs.org/doi/abs/10.1021/acs.jpcb.5b02536

2.1 Introduction

Hydrogen sulfide (H2S) is a very hazardous compound; its safe and efficient handling

poses a tremendous challenge to oil and gas industries. For large-scale sweetening of nat-

ural gas, highly energy-intensive amine-based absorption processes are employed. [42] The

resulting acid gas stream is either reinjected into reservoirs or used for sulfur recovery us-

ing the Claus process. [43] In order to meet the emission regulations for the off gases from

the Claus unit, expensive tail gas treatment such as sub-dewpoint processes or amine-

based absorptive separation is employed. [43] Innovative solutions for these separations

are of immense environmental and economic interest. Considering the health hazards of

H2S, with concentrations as low as 500 ppm being fatal, [44] predictive molecular mod-

eling may prove instrumental for providing molecular-level insights and for guiding the

10

https://pubs.acs.org/doi/abs/10.1021/acs.jpcb.5b02536

https://pubs.acs.org/doi/abs/10.1021/acs.jpcb.5b02536

Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 11

development of improved separation processes, but the success of such modeling studies

hinges on the availability of accurate force fields to describe the systems of interest.

Molecular simulations of systems containing H2S have been carried out for almost

three decades. In 1986, Jorgensen [45] proposed the first force field to describe H2S: a

three-site model developed to reproduce its enthalpy of vaporization and liquid den-

sity at the normal boiling point. However, this model grossly over predicts the vapor

pressure [46] and liquid-phase relative permittivity (RP) [47] of H2S. In 1989, Forester

et al. [48] introduced a four-site model by fitting to the dimer structure predicted by

a distributed-multipole analysis at the 6-31 G* level of theory. However, this force

field results in a significant under-estimation of the vapor pressure. [46] Subsequently

in 1997, Kristóf and Liszi [46] reparametrized the four-site model of Forester to accu-

rately reproduce the vapor–liquid coexistence curve (VLCC) of H2S. The liquid-phase

RP for this model at T = 212 K is 16.1 compared to the experimental value of 8.04. [49]

Also, this model overestimates the strength of the interactions between H2S and CO2

when binary phase equilibria are simulated. In 2000, Delhommelle et al. [50] stressed the

need for a polarizable force field for H2S to better predict binary phase equilibria for

polar/non-polar mixtures, and proposed a five-site polarizable model for H2S to improve

pressure-composition curves for binary mixtures of H2S and n-pentane. In an attempt

to develop an atom-based force field, Nath developed a three-site model. [51] This model

predicts with good accuracy the phase equilibria of H2S with higher alkanes, but it un-

derestimates the boiling point by 7 K. Kamath et al. [52] proposed four models in 2005,

each of them being a three-site model with varying values of the partial charges. RP

values at T = 194.6 K for their models A, B, C, and D are 8.2, 20.4, 30, and 37, re-

spectively, while the experimental value is 8.99 [49] at this temperature. In a subsequent

paper by Kamath and Potoff, [53] the deficiency of their H2S model to correctly estimate

the interactions between CO2 and H2S has been highlighted. These authors mention

that induced polarization effects are not expected to significantly improve the predicted

phase behavior for the H2S/CO2 system because of the relatively small dipole moment

of H2S. More recently, Drude-polarizable force fields for H2S have been proposed. [47,54]

In this work, we seek an H2S model for the Transferable Potentials for Phase Equilib-

ria (TraPPE) force field that overcomes prior deficiencies and more accurately describes

the interactions of H2S with CO2 and CH4 that are pivotal for modeling of sour gas


mixtures. Targets for our force field include: reproducing the experimental critical tem-

perature of H2S within 1%, its saturated liquid density at the normal boiling point within

1%, its saturated vapor pressures over the complete VLCC range within 10%, and the

compositions in binary vapor–liquid equilibria (VLE) with CO2 and CH4 within an av-

erage deviation of less than 5% using standard combining rules for unlike interactions.

To our knowledge, none of the available force fields in the literature meet all of these

constraints. Furthermore, the performance of the resulting model is also assessed via

other condensed-phase properties and the prediction of the triple point temperature.

2.2 Force Fields

The H2S models developed and assessed in this work and also the TraPPE all-atom mod-

els [35,55] for CO2 and CH4 are non-polarizable and have a rigid geometry. The internal

geometry of the H2S model is the same as the model by Jorgensen. [45] Bond lengths

and bond angles for molecules investigated here are listed in Table 2.1. Non-bonded

interactions are modeled using a pairwise-additive potential consisting of Lennard-Jones

(LJ) 12–6 and Coulomb terms:

U(rij) = 4εij

[(σijrij

)12

−(σijrij

)6]

+qiqj

4πε0rij, (2.1)

where rij , εij , σij , qi, and qj are the site-site separation, LJ well depth, LJ diameter,

and partial charges for beads i and j, respectively. In order to allow applicability over a

wide spectrum of potential compositions of natural gas streams and also for the sake of

consistency with other TraPPE models, the standard Lorentz-Berthelot combining rules

are used for all unlike interactions: [56]

σij =σii + σjj

2and εij =

√εiiεjj . (2.2)

2.2.1 Model Development

This subsection describes four different models for H2S that are explored in our effort to

extend the TraPPE force field to H2S. Broadly, two variations and their combinations are


Table 2.1: Bond lengths and bond angles for TraPPE models

molecule bond type length angle type angle[Å] [deg]

H2S rH−S 1.34 ∠ HSH 92CH4 rC−H 1.10 ∠ HCH 109.4712CO2 rC−O 1.16 ∠ OCO 180

explored: (i) the charge distribution and (ii) the molecular shape as defined by the LJ

interactions. Shifting the partial negative charge from the location of the S atom (where

it is placed for models with three interaction sites) to an additional off-atom X-site on the

H-S-H angle bisector and placed toward the H atoms (for models with four interaction

sites) allows one to explore the effects of changing the charge distribution and adjusting

the ratio of dipole to quadrupole moments of H2S. As far as changing the molecular

shape through the LJ interactions is concerned, additional LJ sites can be placed on the

H atoms in addition to the S atom to account for the non-spherical shape of the H2S

molecule. Exploring the two variations results in four different model types, which are

illustrated in Figure 2.1. Here, type A-B corresponds to a model with A interaction sites

and B LJ interaction centers. For instance, type 4-3 implies four interaction sites with

three LJ interaction sites placed on the atomic positions and three partial charges placed

on the locations of the H atoms and the off-atom X site. This 4-3 model requires fitting

of four LJ parameters (for the sites placed on H and S atoms), one X-site displacement

(for the distance between S atom and X site), and the partial negative charge on the X

site (where the constraint of molecular neutrality requires qX = −2qH). In principle, one

could also construct four-site models with partial charges and/or LJ sites placed on all

four sites. This would significantly expand the parameter space because it would allow

for two adjustable parameters for partial charges and two additional LJ parameters, but

such models are not considered in order to limit the already high dimensional parameter

space (6-dimensional for the 4-3 model) to be explored for a wide range of properties.

Model Type 3-1

Type 3-1 is the simplest of all models and consists of three sites with partial charges

and a single LJ site located at the sulfur atom. In this case, there are three parameters


Figure 2.1: Schematic representation of the types of H2S models. Type A-B implies anA-site model with B LJ interaction sites. Yellow, black, and cyan spheres represent theS atom, H atoms, and the off-atom X site, respectively.

Table 2.2: Force field parameters: partial charges (qi), LJ parameters (εii and σii), anddisplacement (δS−X) of off-atom X site.molecule reference model qS qX εSS/kB σSS εHH/kB σHH δS−X

[|e|] [|e|] [K] [Å] [K] [Å] [Å]H2S Kamath et al. [52] 3-1 −0.252 278 3.71H2S this work 3-1 −0.25 278 3.71H2S Kristof & Liszi 4∗-1 +0.40 −0.90 250 3.73 0.1862H2S this work 4-1 −0.64 248 3.75 0.5H2S Nath [51] 3-3 −0.248 250 3.72 3.9 0.98H2S this work 3-3 −0.28 125 3.60 50 2.5H2S this work 4-3 −0.42 122 3.60 50 2.5 0.3

εCC/kB σCC εC−H/kB σC−H

CH4 TraPPE–EH 0.01 3.31 15.3 3.31qC εCC/kB σCC εOO/kB σOO

CO2 TraPPE +0.70 27 2.80 79 3.05

(εSS, σSS, and qS) that need to be optimized. Screening models for the liquid-phase

RP reveals that this property is not very sensitive to the LJ parameters (as long as the

density is close to the experimental value), but is almost entirely determined by the

partial charges. A qS value between −0.25 and −0.26 |e| results in a reasonable RP for

the model. Having settled on a value for qS, LJ parameters are optimized to fit to the

critical temperature, saturated vapor pressures, and liquid densities. The parameters

given in Table 2.2 are only a representative set of the many type 3-1 models possible

with −0.26|e| ≤ qS ≤ −0.25|e|. These parameters are close to one of the four H2S force

fields proposed by Kamath et al. [52]


Model Type 4-1

To study the effect of changing the ratio of dipole to quadrupole moments of H2S, the

negative charge can be shifted from S by a distance δS−X towards the H atoms along

the H-S-H angle bisector. The type 4-1 model requires optimization of four parameters

(εSS, σSS, qX, and δS−X). The van der Waals interactions continue to be modeled using

a single LJ site on the S atom. Once again, the liquid-phase RP is found to be fairly

insensitive to the LJ parameters (as long as the liquid density is well reproduced), but

mostly determined by qX and δS−X. Multiple combinations of qX and δS−X yield an

accurate liquid-phase RP. For each combination, the LJ parameters were obtained by

fitting to the critical temperature and liquid density, and the four-parameter combination

resulting in the correct slope of logarithmic pressure versus inverse temperature line is

used to obtain the optimized set of parameters listed in Table 2.2.

Model Type 3-3

Model type 3-3 differs from type 3-1 by additional LJ sites on the H atoms. Distributing

the van der Waals interactions helps to effectively capture the shape of the H2S molecule.

The 3-3 model requires optimization of five parameters: εSS, σSS, εHH, σHH, and qS.

Given a reasonable set of LJ parameters, the partial charges can again be adjusted by

fitting to the liquid-phase RP. Since the binary VLE for CO2/H2S mixture is quite

sensitive to σHH and εHH, this property dominates the choice of LJ parameters for the

H atom. Finally, the LJ parameters for S are fitted to reproduce the single component

VLE of H2S. Multiple iterations of the two sets of LJ parameters are required to reach a

complete set of parameters that can describe all the properties of interest. The optimized

set of parameters for the proposed 3-3 model are listed in Table 2.2. This type is similar

to the atom-based force field of Nath, [51] but smaller values of the LJ well depth and

diameter on the H atom could not yield a satisfactory normal boiling point for three-

site models. Larger LJ parameters used in this work are mainly the result of fitting to

the binary VLE with CO2. Although an extensive parametrization is performed, it is

important to note that relatively large steps are used in obtaining the LJ parameters

for hydrogen (∆σHH = 0.5 Å and ∆εHH/kB = 10 K) because five parameters need

to be optimized simultaneously and the properties involved in fitting are expensive to


compute.

Model Type 4-3

With six parameters (εSS, σSS, εHH, σHH, qX, and δS−X) to be optimized, the 4-3 model

is the most complex of the four models investigated in this work. Although the 4-1

model performs very well for pure component properties, it shows large deviations for

the H2S/CO2 binary mixture. Again, as also for the 3-3 model, distributing the LJ

interactions over both S and H atoms allows one to adjust the strength of the H2S/CO2

interactions. In combination with the adjustments of the dipole moment/quadrupole

moment ratio through the δS−X parameter and the corresponding partial charges, the

4-3 model can be parameterized to satisfy the accuracy requirements for all of the target

properties. The parameters for this model are reported in Table 2.2.

2.2.2 Methane and Carbon Dioxide

The explicit-hydrogen version of the TraPPE force field [35] is used for the CH4 molecules.

This is a rigid five-site model with LJ interaction sites representing the valence electrons

placed on each C–H bond center and an additional LJ site with a very shallow well for

the core electrons on the C atom. CO2 is modeled as a rigid, three-site molecule with LJ

interaction sites and partial charges on each of the three atoms with parameters taken

from the existing TraPPE force field. [55] Force field parameters for both CH4 and CO2

are listed in Table 2.2.

2.3 Simulation Methodology

Gibbs Ensemble Monte Carlo (GEMC) simulations [31,40,57] in the canonical (NV T )

ensemble are used to simulate pure, binary (H2S/CH4 and H2S/CO2), and ternary

H2S/CO2/CH4 VLE. For binary systems, one has the freedom to choose between the

NpT or NV T ensemble due to the additional degree of freedom. However, due to its

easier set-up, the NV T ensemble is used in this work for the binary VLE simulations.

A system size of 1000 total molecules is used for all GEMC simulations of unary, binary,

and ternary systems. Following the standard for the TraPPE force field, LJ interactions

are truncated at 14 Å and analytical tail corrections are applied (this rcut value is slightly


larger than those used for the development of the CH4 and CO2 models). The Ewald

summation method [33] with a screening parameter of κ = 3.2/rcut and Kmax = κLbox +1

for the upper bound of the reciprocal space summation is used for the calculation of the

Coulomb energy. The total system volume is adjusted for each state point to yield a

vapor phase containing about 20% of the molecules. [58] Since this can lead to rather

large volumes (and, correspondingly, linear dimensions) of the vapor-phase box, rcut for

the vapor phase is set to approximately 40% of the box length to reduce the cost of

the Ewald sum calculations. Four kinds of Monte Carlo moves, including translational,

rotational, volume exchange, and particle transfer moves, are used to sample the phase

space. The coupled-decoupled configurational-bias Monte Carlo algorithm [59] is used to

enhance the acceptance rate for particle transfer moves. The probabilities for volume

and transfer moves are set to yield approximately one accepted move of each type per

Monte Carlo cycle (MCC), [58] where a MCC consists of N = 1000 randomly selected

moves. The remaining moves are divided equally between translations and rotations. An

equilibration period of 50,000 to 100,000 MCCs is used for all simulations, and between

100,000 and 200,000 MCCs are used for the production phase.

The static RP values of the liquid and solid phases are calculated from fluctuations

of the system dipole moment sampled during a canonical-ensemble simulation [60]:

εD = 1 +1

3ε0kBV T

(〈M2〉 − 〈M〉2

), (2.3)

where M , ε0, and T are the total system dipole moment, the permittivity of free space,

and the absolute temperature, respectively; V is the volume of the simulation box that

is determined from a prior simulation. For the liquid phase, the equilibrium density

for the model system is obtained by performing an isotropic NpT simulation [61] for

500 molecules at T = 194.6 K and p = 1 atm. For the solid phase, the simulation is

initiated with 500 molecules placed on Fm-3m lattice sites with a 5 × 5 × 5 supercell,

and an anisotropic (orthogonal) NpT simulation, [62] allowing the cell lengths to relax

independently, but maintaining the cell angles orthogonal, is carried out at T = 157.9 K

and p = 1 atm. After equilibration for 100,000 MCCs, the solid is found to maintain

its face-centered cubic structure and the average density is obtained from a production

period of 100,000 MCCCs. The average densities obtained for the liquid and solid


phases are then used for the subsequent canonical-ensemble simulations to determine

the corresponding static RP via Equation 2.3. These simulations consist of equilibration

and production periods of 50,000 and 100,000 MCCs, respectively. For the isobaric-

isothermal simulations, the probability of volume moves is set to result in approximately

one accepted move per MCC and the remaining moves are divided equally between

rotations and translations, as is also done for the canonical-ensemble simulations. In

addition, anisotropic (orthogonal) NpT simulations are carried out to obtain the lattice

parameter at T = 142 K and p = 1 atm.

Isobaric–isothermal ensemble simulations are performed with 500 molecules at T =

298 K and p = 31 bar to obtain the intermolecular radial distribution functions at the

same conditions as the experimental data. [63] The system is equilibrated for 100,000

MCCs, followed by a production run of 200,000 MCCs.

To determine the triple point, Gibbs ensemble Monte Carlo simulations, [31,40,57,64]

are extended to cover solid–vapor equilibria and metastable states on the VLCC using a

slab set-up introduced by Chen et al. [65] In this set-up, the condensed-phase simulation

box contains a slab of material surrounded by vapor and the other box contains a

homogeneous vapor phase; the condensed-phase box is elongated along the z-axis and

includes two surfaces parallel to the xy-plane. These simulations are started using a

solid slab consisting of 2744 molecules (7 x 7 x 14 unit cells) and an empty vapor box.

The vapor box volume is adjusted for each temperature to yield about 100 molecules

in the vapor phase at equilibrium. For the condensed-phase box, volume changes are

carried out by randomly changing one of the cell length while keeping the orthogonal

shape. Again, the fraction of moves are adjusted to yield about one accepted volume and

one accepted particle swap move per cycles with the remainder divided equally between

translations and rotations. Due to the heterogeneous nature of the condensed-phase box,

LJ tail corrections are not applied but a larger cut-off at 19 Å is used together with the

Ewald summation for the Coulomb interactions. After equilibration for at least 50,000

MCCs, data is collected from production periods ranging between 400,000 to 600,000

MCCs for the different simulation temperatures.

For all systems investigated in this work, eight independent Monte Carlo simulations

are carried out and the statistical uncertainties reported in the following sections are the

standard errors of the mean calculated from these independent simulations.


For the calculation of self-diffusion coefficient, liquid density is first obtained using

Monte Carlo simulations in the NpT ensemble at T = 206.5 K and p = 1 atm. Using this

density as input for a 1000-particle system, a molecular dynamics run (with the GRO-

MACS 4.6.3 software [66,67] and the SHAKE algorithm for the rigid-body constraints [68])

in the canonical ensemble of 1 ns in duration is used for equilibration. This is followed

by a 10 ns trajectory in the microcanonical ensemble. The self-diffusion coefficient is

computed from a linear fit to the mean square displacement versus time (using multiple

time origins) to only the region from 0.5 to 3.5 ns of the trajectory to avoid contami-

nation from the initial ballistic region and insufficient statistics toward the end of the

simulation. The error is estimated by dividing the trajectory into two parts.

2.4 Results and Discussion

2.4.1 Liquid-Phase Relative Permittivity

The liquid-phase RP is a convenient measure of the polarity of a solvent. Due to induced

polarization effects, the (average) charge distribution of a molecule in a condensed-phase

environment differs from the distribution found for an isolated molecule in the gas phase.

Thus, non-polarizable models usually employ a larger dipole moment than present in the

gas phase. It should be noted, however, that the liquid-phase RP depends not only on

the molecular dipole moment but also reflects the degree of orientational ordering in

the liquid. For weakly dipolar molecules, such as H2S, the computation of the liquid-

phase RP is relatively inexpensive compared to the computation of binary vapor-liquid

equilibria with a non-polar molecule. Thus, evaluation of the liquid-phase RP is used

here to quickly narrow the range of partial charges for a given type of H2S model. The

static dipole moments for the four types of models optimized in this work are listed in

Table 2.3. As can be seen, the µD values for three of the models are about 30% larger

than the experimentally determined gas-phase value of 0.98 D. [69] The exception is the

3-1 model for which compromises need to be made to achieve a reasonable VLCC (see

below). The liquid-phase RP values at T = 194.6 K and p = 1 atm (i.e., close to the

triple point) for the other three models are found to deviate by less than 4% from the

experimental value of 8.99, [49] whereas the 3-1 model yield a value of only 8.0. Overall, it

is clear that computation of the liquid-phase RP helps to constrain the range of suitable


Table 2.3: Dipole moment, liquid-phase density, and relative permittivity at 194.6 Kand 1 atm.

model µD ρliq εD

[D] [g/ml]

3-1 1.12 0.9681 8.01

4-1 1.32 0.9741 9.21

3-3 1.25 0.9751 9.31

4-3 1.27 0.9771 8.71

Expt. 0.98 [69] 0.981 [70] 8.99 [49]

Subscripts denote the standard error of the mean for the last digit(s).Superscripts denote the sources for the experimental data.

force field parameters, but it is not sufficient to discard specific model types.

2.4.2 Unary Vapor–Liquid Equilibria

Vapor–liquid coexistence curves and Clausius-Clapeyron plots for all four models are

shown in Figures 2.2 and 2.3 (and numerical data are provided in Tables S1-S2 in

the Supporting Information),1 respectively, and numerical values of the normal boil-

ing points, critical properties, and accentric factors for these models are summarized

in Table 2.4. For the calculation of the critical properties, saturated liquid and vapor

densities are fitted to the scaling law for the critical temperature [71]

ρliq(T )− ρvap(T ) = A(T − Tc)β (2.4)

and the law of rectilinear diameters [72]

ρliq(T ) + ρvap(T )

2= ρc +B(T − Tc) (2.5)

where β = 0.326 is the universal critical exponent for three-dimensional systems. The

critical pressure is determined by extrapolation of the saturated vapor pressures to to

the computed critical temperature using the Antoine equation. Only VLCC data at

T ≥ 340 K (i.e, T ≥ 0.9Tc) are used for the determination of the critical point. The1https://pubs.acs.org/doi/suppl/10.1021/acs.jpcb.5b02536/suppl_file/jp5b02536_si_001.

pdf

https://pubs.acs.org/doi/suppl/10.1021/acs.jpcb.5b02536/suppl_file/jp5b02536_si_001.pdf

https://pubs.acs.org/doi/suppl/10.1021/acs.jpcb.5b02536/suppl_file/jp5b02536_si_001.pdf


0.0 0.2 0.4 0.6 0.8 1.0

ρ [g/ml]

200

240

280

320

360

T [

K]

Beaton et al.

Cubitt et al.

Goodwin

Reamer et al.

3-1 model

4-1 model

3-3 model

4-3 model

Figure 2.2: Vapor–liquid coexistence curves for hydrogen sulfide. Experimental data byBeaton et al., [73] Cubitt et al., [74] Goodwin, [70] and Reamer et al., [75] are representedby black plusses, diamonds, squares, and crosses. The orange up triangles, green downtriangles, magenta left triangles, and cyan right triangles show the simulation results forthe 3-1, 4-1, 3-3, and 4-3 models, respectively. Statistical uncertainties for the simulationdata are smaller than the symbol size.

normal boiling point is obtained by interpolation of the saturated vapor pressures using

the Clausius-Clapeyron equation for only the two data points closest to Tb.

With the exception of the type 3-1 model, the other three models allow for a very

accurate description of the unary VLE of H2S. The 3-1 model is highly simplified and,

with the constraint of yielding an acceptable liquid-phase RP, is incapable of capturing

the correct dependence of p on T (see Figures 2.3 and 2.4), and the best parameterization

yields a 3-1 model that underestimates Tb but overestimates Tc and pc. As a result, the

3-1 model qualitatively fails for the accentric factor that is under predicted by an order

of magnitude. The 3-1 model also yields larger deviations for the orthobaric liquid

density and significantly under predicts the enthalpy of vaporization at T ≤ 320 K (see


3 4 5

1000/T [K-1

]

3

4

5

6

7

8

9

ln (

p [kP

a])

Clarke & Glew

Cubitt et. al.

Goodwin

Reamer et al.

3-1 model

4-1 model

3-3 model

4-3 model

Figure 2.3: Saturated vapor pressure versus inverse temperature for hydrogen sulfide.Symbol styles and colors as in Figure 2.2. Statistical uncertainties for the simulationdata are smaller than the symbol size.

Figure S1 and Table S3 in the Supporting Information). It should be noted here that

the parameters of the 3-1 model found in this work are nearly the same as for model A

developed by Kamath et al. [52] However, the normal boiling point and critical properties

reported here are somewhat different, likely due to the use of a larger cut-off in this work

(14 versus 10 Å) and the inclusion of only near-critical data for the determination of the

critical point in this work (T ≥ 0.9Tc versus T ≥ 0.7Tc); the applicability of the Ising

scaling law far away from Tc is questionable particularly for polar compounds. Based

on the deficiencies of the 3-1 model for the computation of the unary VLE, this model

is abandoned and not considered for the calculation of other properties.

For the 4-1, 3-3, and 4-3 model types, parameters can be found that satisfy the

target accuracy for the unary VLE of H2S. The normal boiling point [70,74] is reproduced

to within 0.2% (just outside of the statistical uncertainties) by all three models, and

the saturated vapor pressures for all three models fall within 5% of the experimental

values over the entire stability range of the liquid phase (see Figure 2.4). All three


Table 2.4: Normal boiling point, critical properties, and accentric factor for hydrogensulfide.

model Tb Tc ρc pc ω[K] [K] [g/cc] [bar]

3-1 206.91 378.85 0.3542 953 0.0094

4-1 213.32 377.06 0.3602 934 0.0814

3-3 212.62 375.75 0.3602 943 0.0873

4-3 212.62 374.56 0.3612 933 0.0923

expt 212.85 [74] 373.07 [76] 0.348 [70] 89.46 [76] 0.096 [70]

212.87 [70] 373.32 [77] 0.349 [78] 89.7 [74]

373.4 [70] 90.05 [77]

373.54 [78] 90.07 [78]


models slightly underpredict the orthobaric liquid density for T < 300 K, whereas it is

overpredicted in the near-critical region. The 4- 3 model is slightly more accurate for

ρliq over the full temperature range than the 4-1 and 3-3 models. The three models

also slightly overpredict the enthalpy of vaporization (see Figure S1 and Table S3 in the

Supporting Information). The critical temperature is overestimated by 1%, 0.7%, and

0.3% for models 4-1, 3-3, and 4-3, respectively. The critical pressures determined for

these three models are very close to each other but fall about 4% above the average of

the experimental values. [74,76–78] Similarly, the critical densities for the three models are

very close to each other but are about 3% higher than the experimental values. [70,78]

The 4-3 model yields a more accurate accentric factor than the 4-1 and 3-3 models.

The ability of the 4-1, 3-3, and 4-3 types of models to reproduce the unary VLE and

the liquid-phase RP of H2S indicates that either adjusting the dipole/quadrupole ratio

or capturing the non-spherical shape of the H2S molecule provides sufficient flexibility

for the model parameterization when only considering these properties. Thus, additional

experimental data are needed to select the best model. Here, it is found that the binary

VLE of H2S/CO2 can help to resolve this issue.


180 200 220 240 260 280 300 320 340 360

T [K]

-5

0

5

10

15

% ∆

p

-2

0

2

4

6

% ∆

ρli

q

Goodwin

3-1 model

4-1 model

3-3 model

4-3 model

Figure 2.4: Relative deviations in orthobaric liquid density and saturated vapor pressurefrom the recommended experimental values [70] as a function of temperature. Symbolstyles and colors as in Figure 2.2. Statistical uncertainties for the simulation data aresmaller than the symbol size.

2.4.3 Binary Mixture with Carbon Dioxide

Carbon dioxide and hydrogen sulfide constitute a large fraction of the waste streams

resulting from oil and gas sweetening. These compounds can be reinjected into reservoirs

either as compressed vapors or as liquified acidic streams through compression followed

by cooling. These processes have aroused significant interest in the determination of the

binary CO2/H2S VLE. Already in 1953, Bierlein and Kay [79] reported on measurements

of the binary VLE in the temperature range from 273 to 333 K. This was followed in 1959

by the work of Sabocinski and Kurata [80] covering a wider range of 225 K ≤ T ≤ 364 K.


Recently, Chapoy et al. [81] reported binary data for 258 K ≤ T ≤ 313 K. Considering

the practical importance of this system and also for improving the transferability of the

H2S force field, binary VLE for the H2S/CO2 mixture are considered as an additional

criterion in the force field development.

The critical temperatures of CO2 and H2S are 304 and 373 K, respectively. Thus,

T = 293.16 and 333.16 K were selected for the calculation of the binary VLE to include

data below and above the critical temperature of the low-boiling component (CO2) and

because two experimental data sets are available at these temperatures. Figures 2.5 and

2.6 show the pressure-composition diagrams and separation factors for the CO2/H2S

mixture at 293.16 K and 333.16 K, respectively. The pxy data for the 4-1 model are

shifted significantly to the right (i.e., higher CO2 mole fractions for both phases at

a given pressure) than the experimental data, whereas the data for the 3-3 and 4-3

models follow closely the experimental data. This behavior implies that the 4-1 model

somewhat over predicts the strength of the H2S/CO2 interactions. Actually, the data

for the 4-1 model closely match the predictions from the Peng-Robinson equation of

state [82] with the kij parameter set to zero, whereas kij = 0.0960 is required to correlate

the experimental data at T = 293 K. [81] Apparently, the 3-3 and 4-3 models are able

to capture this positive deviation from regular mixing that requires a weakening of the

unlike interactions. The deviations for the separation factor are significantly smaller

with the 4-1 model under predicting the separation factor at lower CO2 mole fraction

(xCO2 < 0.5 at T = 293.16 K and xCO2 < 0.25 at T = 333.16 K) and over predicting at

higher mole fractions, whereas the 3-3 and 4-3 models perform better at low and high

CO2 mole fractions (but of course not at the point where the data for the 4-1 model

intersect the experimental data).

In order to correctly predict the binary VLE for the H2S/CO2 mixture with non-

polarizable models, the key ingredient that is missing in most models in the literature

is accounting for the non-spherical repulsive shape of the tri-atomic H2S molecule which

requires additional LJ sites on the hydrogen atoms. The H2S force field by Nath includes

these additional LJ sites, but both the LJ diameter and well depth are too small (see

Table 2.2) to yield a satisfactory representation of the unlike interactions. [51] It is found

here that relatively large values for the σHH and εHH parameters are essential to fit the

binary VLE with CO2. Figure 2.7 illustrates the [H](H2S)–[O](CO2) radial distribution


0.0 0.2 0.4 0.6 0.8 1.0

xCO

2

, yCO

2

10

20

30

40

50

60

p [

ba

r]

0.2 0.4 0.6 0.8 1.0x

CO2

0.0

0.2

0.4

0.6

0.8

yC

O2

Bierlein & Kay

Chapoy et al.

4-1 model3-3 model4-3 model

Figure 2.5: Pressure–composition diagram (top) and separation factor (bottom) for theH2S/CO2 mixture at T = 293.16 K. The experimental data of Bierlein and Kay [79] andof Chapoy et al. [81] (at T = 293.47 K) are shown as crosses and stars, respectively. Thegreen up triangles, magenta left triangles, and cyan right triangles depict the computeddata for the 4-1, 3-3, and 4-3 models, respectively.


0.0 0.1 0.2 0.3 0.4 0.5 0.6

xCO

2

, yCO

2

40

50

60

70

80

p [

ba

r]

0.1 0.2 0.3 0.4 0.5 0.6x

CO2

0.0

0.1

0.2

0.3

0.4

0.5

yC

O2

Bierlein & Kay

Sabocinski & Kurata4-1 model3-3 model4-3 model

Figure 2.6: Pressure–composition diagram (top) and separation factor (bottom) for theH2S/CO2 mixture at T = 333.16 K. The experimental data of Kay and Bierlein [79] andof Sobocinski and Kurata [80] are shown as crosses and stars, respectively. Symbols andcolors for the simulation data as in Figure 2.5.

functions (RDF) and the corresponding number integrals (average number of [O] atoms

surrounding a given [H] atom) for the 4-1, 3-3, and 4-3 models at a state point where


2 3 4 5 6 7

r [Å]

0.00

0.25

0.50

0.75

1.00

1.25

g (

r)

4-1 model

3-3 model

4-3 model

2 3 4

r [Å]

0

1

2

Nin

t

Figure 2.7: [H](H2S)–[O](CO2) radial distribution function and the corresponding num-ber integrals at T = 293.16 K and xCO2 ≈ 0.45 for the 4-1, 3-3, and 4-3 models shownas green, magenta, and cyan lines, respectively.

the liquid phase is close to equimolar. The RDF for the 4-1 model shows a shoulder for

separations smaller than 3 Å, whereas the corresponding shoulder is shifted to larger

separations by about 0.5 Å for the 3-3 and 4-3 models. As can be seen from the number

integrals, these shoulders account for the nearest neighbor oxygen atom around a given

hydrogen atom. This peak represents a weak hydrogen bond that is further weakened

by the LJ site on the hydrogen donor atom for models 3-3 and 4-3. Based on the

difference in the LJ diameter between an oxygen atom in CO2 (but similar values are

common for water and alcohol models), one can expect that the S–H distance cut-off for

a hydrogen bond should be larger by ≈ 0.3 Å than the commonly used value of 2.6 Å

for O–H distances. [83] The weakening of the hydrogen bond for the 3-3 and 4-3 models

decreases the solubility of carbon dioxide in the H2S liquid phase and, hence, allows one

to reproduce the positive deviations from regular mixing.

As mentioned above, the Lorentz–Berthelot combining rules are used here consis-

tently to compute the LJ parameters for unlike interactions belonging to the same type

of molecule or to two different types of molecules. Other combining rules are available


that yield a larger value for the unlike LJ diameter and a smaller value for the unlike well

depth than the Lorentz– Berthelot combining rules when applied to sites with different

LJ diameters. [56] Use of these different combining rules for the S(H2S)–C(CO2), S(H2S)–

O(CO2), H(H2S)–C(CO2), and H(H2S)–O(CO2) interactions would indeed significantly

weaken the interactions between H2S and CO2 molecules: e.g., by more than 29% and

17% for the S(H2S)–C(CO2) and S(H2S)–O(CO2) well depth, respectively, with the 4-1

model using the Waldman–Hagler rules, i.e., much more than the 10% adjustment re-

quired for the Peng–Robinson equation of state. [81] However, an even bigger effect would

be observed for the S(H2S)–H(H2S) unlike interaction that would require significant repa-

rameterization of the 3-3 and 4-3 H2S models (and also of the TraPPE CH4 model) and

to a lesser extent of the TraPPE CO2 model. Such a complete reparameterization is

beyond the scope of the present work.

Based on its failure to predict the H2S/CO2 VLE with satisfactory accuracy, the 4-1

model is abandoned at this point. However, neither the binary VLE nor the structural

data for this mixture exhibit a significant difference between the 3-3 and 4-3 models,

and additional properties are needed to decide between these models.

2.4.4 Binary Mixture with Methane

Methane is the major component (in terms of mole fraction) of natural gas and, hence,

accurately describing the H2S/CH4 binary VLE is also of paramount importance for the

development of the H2S force field. Methane’s critical temperature of 190.6 K falls only

slightly above the triple point of H2S (187.6 K) and, hence, simulations for the H2S/CH4

mixture are performed only for Tc(CH4) < T < Tc(H2S). The pressure–composition

diagrams and separation factors at T = 277.60 and 310.94 K predicted with the 3-3

and 4-3 models for this mixture are compared to the experimental data by Reamer

et al. [75] in Figure 2.8. Both force fields accurately predict the binary VLE at both

temperatures and there are no significant differences between the models. This should

not come as a surprise because the LJ parameters for these two models are very similar

(see Table 2.2). Clearly, using the liquid-phase RP in the parameterization procedure

sufficiently constrained the LJ parameter space to yield a good balance of Coulomb

(including the increased dipole moment due to polarization in polar environments) and

LJ contributions to the cohesive energy.


0.0 0.2 0.4 0.6 0.8

xCH

4

, yCH

4

0

20

40

60

80

100

120

140

p [

ba

r]

Reamer et al. (277.60 K)

Reamer et al. (310.94 K)

3-3 model (277.60 K)

4-3 model (277.60 K)

3-3 model (310.94 K)

4-3 model (310.94 K)

0.0 0.2 0.4 0.6 0.8x

CH4

0.2

0.4

0.6

0.8

yC

H4

Figure 2.8: Pressure–composition diagram (top) and separation factor (bottom) for theH2S/CH4 mixture at T = 277.60 and 310.94 K. For 277.60 K, the experimental dataof Reamer et al. [75] and the computed data for the 3-3 and 4-3 models are shown asblack crosses, magenta left triangles, and cyan right triangles, respectively, and thecorresponding data for 310.94 K are depicted as black stars, magenta down triangles,and cyan up triangles, respectively.


Figure 2.9: Ternary phase diagram of CH4/CO2/H2S system at T = 238.76 K andp = 34.47 bar. Simulation results and experimental data [84] are shown as open and filledsymbols, respectively.

2.4.5 Ternary Mixture with Methane and Carbon dioxide

Ternary mixtures involving CH4, CO2, and H2S are of considerable importance in design-

ing new processes for natural gas sweetening. To further assess the predictive capabilities

of the TraPPE force field, the ternary phase diagram for the H2S/ CO2/CH4 mixture at

T = 238.76 K and p = 20.68, 34.47, and 48.26 bar (also see SI) are computed. In this

case, TCH4c < T < TCO2

c < TH2Sc . The coexistence data at the intermediate pressure are

presented in Figure 2.9 along with a comparison to the experimental data from Hensel

and Massoth [84] (data for the other two pressures are provided in the Supporting Infor-

mation). Overall, the predictions are in close agreement with the experimental data for

all pressures, but the CH4 mole fraction is slightly overestimated in the vapor phase and

underestimated in the liquid phase.

2.4.6 Liquid-Phase Radial Distribution Functions

Next we considered the liquid-phase structure of pure H2S in the hope that the difference

in the dipole-quadrupole ratio for the 3-3 and 4-3 models would result in an appreciable


Table 2.5: Liquid-phase density, calculated self-diffusion coefficient for a 1000-particlesystem, and extrapolated bulk-limit self-diffusion coefficient at 206.5 K and 1 atm.

model ρliq [g/mL] D1000 [10−5 cm2/s] D∞ [10−5 cm2/s]

3-1 0.9481 3.21 3.51

4-1 0.9542 3.21 3.51

3-3 0.9562 3.42 3.72

4-3 0.9582 3.22 3.52

expt 0.960 [70] 3.72[85]


difference in the local structure. However, as can be seen from the data presented in

Figure 2.10, both models yield RDFs that are nearly indistinguishable. Agreement with

the neutron diffraction data by Santoli et al. [63] for a state point about midway between

triple and critical points is excellent for the S–S and S–H RDFs including the double

peak present in the S–H RDF. For the H–H RDF, the simulation data show the initial

rise at slightly larger separation and the first peak is sharper and higher. These small

deficiencies are due to the use of models with rigid geometry and the neglect of nuclear

quantum effects that both would soften the H–H RDF. Nevertheless, both models are

clearly capable of describing the liquid structure rather well.

2.4.7 Liquid-Phase Self-Diffusion Coefficient

In addition to the thermodynamic and structural properties of H2S, we also calculated

the self-diffusion coefficient of its liquid phase near the normal boiling point (see Ta-

ble 2.5) to assess the performance of the various models developed in this work. Once a

hydrodynamic correction (using the experimental data for the viscosity [70]) is made to

account for finite-size effects, [86,87] then the D∞ values for all models coincide with the

experimental value to within uncertainties. [85] Although the computed D∞ values are

further evidence for the quality of the 4-3 and 3-3 models, they do not allow distinction

between these models.


2 4 6 8 10 12 14

r [Å]

0.00

0.25

0.50

0.75

1.00

1.25

g (

r)

0.25

0.50

0.75

1.00

1.25

g (

r)

Santoli et al.

3-3 model

4-3 model

0.5

1.0

1.5

2.0

2.5

g (

r)

Figure 2.10: Intermolecular radial distribution functions for liquid H2S at T = 298 Kand p = 31 bar: S–S (top), S–H (middle), and H–H (bottom). The experimental dataof Santoli et al. [63] are represented by black circles, and the simulation data for the 3-3and 4-3 models are depicted as magenta solid and cyan dashed lines, respectively.

2.4.8 Solid-Phase Structure and Relative Permittivity

Compared to the extremely complex phase diagram of water, the phase diagram for H2S

is relatively simple. [88] At atmospheric pressure, H2S exhibits three solid phases with

decreasing temperature. [89] The high-temperature solid phase has a face-centered cubic

(FCC) structure with a lattice parameter of a = 5.8054 Å at T = 142 K. [89] Simulations

in the constant-stress ensemble indicate stability of the FCC structure for the 3-3 and

4-3 models, but the lattice parameters are slightly over predicted with a = 5.9012 and

5.891 Å for the 3-3 and 4-3 models, respectively. The computed values of solid–phase


RP at T = 157.9 K are 15.33 and 13.62 for the 3-3 and 4-3 models, respectively, while

the experimental value is 13.7. [49] Compared to the liquid-phase RP at T = 194.6 K (see

Table 2.3), these values represent increases by a factor of 1.65, 1.55, and 1.52 for the

3-3 and the 4-3 models and the experimental measurements, respectively. Thus, the 4-3

model performs slightly better for these solid-phase properties than the 3-3 model.

2.4.9 Triple Point

As discussed in the preceding sections, the 3-3 and 4-3 models perform nearly equally

well for all of the properties involving fluid phases, but differences are more significant

for the solid-phase properties. The key difference between these models is the larger

magnitude of the quadrupole moment for the 4-3 model, whereas their dipole moments

are very similar. Recently, Pérez-Sánchez et al. [90] compared four different CO2 force

fields, found that the TraPPE model performs extremely well in predicting the triple

point, [65] and highlighted the importance of the quadrupole moment for the accurate

prediction of the triple point. Similar observations were made earlier for benzene. [91]

In order to select between the 3-3 and 4-3 models, their solid–vapor equilibria (SVE)

and triple point prediction are considered. Figure 2.11 illustrates the behavior of the

saturated vapor pressures near the triple point. The triple point temperature and pres-

sure is estimated from the intersection of Clausius–Clapeyron lines for the solid–vapor

and vapor–liquid equilibria. In order to account for the different treatment of the LJ

interactions (rcut = 14 Å and tail corrections for the VLE simulations using homoge-

neous phases and rcut = 19 Å without tail corrections for the SVE simulations using the

slab set-up) the VLE vapor pressures are shifted up as follows. The average difference

in potential energies is calculated for liquid-phase configurations using both of these

descriptions for the long-range interactions. The VLE pressures are then scaled up by

the Boltzmann factor resulting from this estimate of the difference in the enthalpy of

vaporization. The uncertainty in the triple point determination is obtained from the

standard error of the mean found by pairing randomly eight independent SVE lines with

eight independent VLE lines and finding eight different intersection points. The result-

ing triple point temperatures and pressures are 174 ± 2 K and 10 ± 2 kPa for the 3-3

model and 184±3 K and 19±4 kPa for the 4-3 model. The latter fall much closer to the

experimental values of 187.6 K and 23.2 kPa, [92,93] and clearly the 4-3 model is superior


4.8 5.2 5.6 6.0 6.4

1000/T [K-1

]

1

2

3

4

ln (

p [

kP

a])

Clark et al.Giauque & Blue

3-3 model4-3 model

Figure 2.11: Clausius–Clapeyron plot of saturated vapor pressure versus inverse temper-ature for the region near the triple point. The experimentally determined triple pointsfrom Clark et al. [92] and Giauque and Blue [93] are shown as the plus and cross symbols.The SVE and VLE data for the 3-3 and 4-3 models are depicted as open magenta left tri-angles and open cyan right triangles, respectively, and the corresponding filled symbolsdenote the triple points. The solid and dashed lines illustrate Clausius–Clapeyron fitsto the simulation data and their extrapolation into the metastable regimes, respectively.

when including properties involving solid phases in the assessment.

For H2S, the slopes of the SVE and VLE lines are very similar, i.e., the difference in

the enthalpies of sublimation and vaporization is small. This makes the determination

of the triple point rather challenging and the statistical uncertainties are large. For an

independent evaluation of the triple point temperature, we also considered structural

information. Visual inspection of the simulation trajectories for the elongated box con-

taining the slab of material (see Figure 2.12) allows one to find the temperature below

which one observes only surface melting and above which the entire slab melts. For the

4-3 model, the slab melts completely at T = 190 K, but a significant crystalline region

in the center of the slab is stable at T = 180 K.

More quantitively, the solid and liquid regions can be determined from evaluation


Figure 2.12: Snapshots of the final configuration from slab simulations for the 4-3 modelat T = 160, 170, 180, and 190 K. For clarity, only the sulfur atoms are shown in aprojection perpendicular to the xy-diagonal.

of a structural order parameter. For the FCC lattice, Huitema et al. [94] suggested the

following Q6 order parameter:

Q6 =

√4π

13{[Re(Q6−6)]2 + [Re(Q60)]2 + [Re(Q66)]2} (2.6)

where Re[Qlm] denotes the real part of Qlm, given by:

Qlm =1

N

N∑j=1

Ylm[θ(rij), φ(rij)] (2.7)

where N is the number of nearest neighbors surrounding atom i, θ(rij) and φ(rij) are the

polar and azimuthal angles of the vector rij with respect to the reference z-axis ((111)

in case of the FCC lattice), and Ylm[θ(rij), φ(rij)] is the spherical harmonic. A spheri-

cal cutoff at 5 Å is used to determine the nearest neighbors because, at this value, the


160 170 180 190

T [K]

0.15

0.20

0.25

0.30

0.35

0.40

Q6

3-3 model

4-3 model

Figure 2.13: Temperature dependence of the slab-averaged FCC order parameter. Thefilled magenta left triangles and filled cyan right triangles show the average values cal-culated from eight independent simulations for the 3-3 and 4-3 models, respectively, andthe corresponding open symbols indicate the largest and smallest values found amongthese independent simulations.

overwhelming majority of molecules in the bulk solid have 12 nearest neighbors (charac-

teristic of the FCC arrangement) and less than 10% of the molecules are surrounded by

a higher number of neighbors contributing to disorder. The value of Q6 is calculated for

each sulfur atom and can then be averaged for specific regions of the slab or using the

entire slab. The value of Q6 for an atom surrounded by nearest neighbors in a perfect

FCC lattice is 0.48476. For liquids, this value remains positive and is close to 0.2 for the

H2S liquid.

The temperature dependence of the Q6 order parameters averaged over the entire

slab for the 3-3 and 4-3 models is illustrated in Figure 2.13. Starting from a temperature

well below the triple point, Q6 initially decreases gradually and then falls steeply as the

triple point is approached. This is due to the fact that, at T = 160 K, the degree

of surface melting is confined to the outermost layer but expands inwards (i.e., more

layers melt) as the triple point is approached (see Figure 2.12 and additional figures for


Q6 as function of z provided in the Supporting Information). Using Q6 ≈ 0.25 as the

boundary between crystalline and liquid slabs (note that this boundary value depends

on the system size because of the fraction of the slab being near the surface decreases as

the system size is increased) yields estimates of the triple point temperature of 173± 2

and 180± 2 for the 3-3 and 4-3 models, respectively, that are consistent with the values

determined from the Clausius–Clapeyron plots.

2.5 Conclusion

The TraPPE force field is extended through the development of the 4-3 model for H2S

that consists of four sites: both sulfur and hydrogen atoms interact via LJ potentials and

partial charges are placed on the hydrogen atoms and an X site located along the H-S-H

bisector. The VLE and liquid-phase RP of H2S are used for the initial parameterization

of the 4-3 model and of three other variants. It is found here that the 3-1 model cannot

satisfactorily reproduce both VLE and liquid-phase RP and that the 4-1 models over

predicts the interactions for H2S–CO2 and fails to reproduce the binary VLE for this

mixture. Although, the 3-3 model performs well for binary mixtures of H2S with CO2 or

CH4, it shows significant deviations for properties involving solid phases including the

triple point and the RP of the FCC solid. Only the 4-3 model yields very good predictions

for the entire set of unary and binary VLE, the liquid- and solid-phase RP, and the triple

point. Furthermore, the 4-3 model reproduce well the liquid-phase structure (as does

also the 3-3 model). It is important to stress here that the new TraPPE 4-3 model does

not rely on any special unlike interactions and the Lorentz-Berthelot combining rules are

used as for the other TraPPE models. Including explicit polarization in a model using

the same number of interactions sites may lead to further gains in accuracy but with a

significant increase in cost.

Chapter 3

Monte Carlo Simulations Probing

the Adsorptive Separation of

Hydrogen Sulfide/Methane

Mixtures Using All-Silica Zeolites

Reprinted with permission from M. S. Shah, M. Tsapatsis, and J. I. Siepmann, Langmuir

2015, 31, 12268–12278. Copyright 2015 American Chemical Society. https://pubs.

acs.org/doi/abs/10.1021/acs.langmuir.5b03015

3.1 Introduction

Hydrogen sulfide is a very toxic gas, and causes irritation to eyes, nose, and throat

at concentrations as low as 5 ppm, and results in an almost instantaneous death at

concentrations above 1000 ppm. [44] Large reserves of natural gas are untapped today

due to the difficulties involved in processing low-quality sour gas. The development

of alkanolamines for acid gas absorption dates back to as early as 1930. [95] Since then,

amine-based regenerative absorption processes, that employ aqueous solutions of organic

amines, have been used for large-scale acid gas sweetening. [96,97] The H2S-rich stream,

generated as a result of this process, is subjected to sulfur recovery in the Claus unit,

39

https://pubs.acs.org/doi/abs/10.1021/acs.langmuir.5b03015

https://pubs.acs.org/doi/abs/10.1021/acs.langmuir.5b03015

Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 40

where H2S is converted to elemental sulfur. Present-day natural gas industries are

facing two main challenges as regards to the sweetening of sour gas. Firstly, with an

increase in the H2S content of newer gas fields, the load on the acid gas treatment

unit is expected to increase dramatically. Secondly, increasingly stringent government

regulations on permissible sulfur emissions may lead to current H2S clean-up strategies

becoming technologically and/or economically insufficient. Thus, as demand for cleaner

energy resources continues to rise and also as the need to explore more difficult, i.e.,

sourer, natural gas reservoirs becomes more pressing, better technologies for efficient

H2S removal will become pivotal.

Adsorptive separations have numerous advantages over absorptive separations: Smaller

foot-print, less exorbitant materials of construction for equipment, and lower pumping

costs are among them. In the last few years, applications of newly discovered nanoporous

materials such as zeolites and metal organic frameworks (MOFs) have demonstrated the

potential for adsorptive separations. [98–100] The structural and chemical stability of ze-

olites over vast ranges of temperature and pressure makes them potential candidates

for separations involving highly corrosive sour natural gas streams. Raw natural gas

emerging from wells often contains a significant amount of water. The gas-phase dipole

moment of water (1.85 D) is about twice that of hydrogen sulfide (0.98 D) and water

forms much stronger hydrogen bonds. Hence, there is a large enthalpic gain for water

to adsorb preferentially over H2S on polar solids, particularly those with the ability to

act as hydrogen bond acceptor or donor, thereby making the adsorption sites largely

unavailable to H2S. However, highly siliceous zeolites (Si/Al ratio tending to infinity)

made with specialized synthesis methods [101] contain negligible amounts of polar cations

and silanol groups, and these materials are extremely hydrophobic. Hence, there is a

potential for all-silica zeolites to selectively capture H2S from natural gas streams.

In this work, adsorption of H2S in seven all-silica zeolite frameworks is investigated

via particle-based Monte Carlo simulations. Selectivity data for H2S over CH4 adsorption

at varying compositions, pressures, and temperatures are presented. The applicability

of ideal adsorbed solution theory (IAST) to H2S/CH4/all-silica zeolite systems at dif-

ferent thermodynamic state points is tested. Finally, to assess the hydrophobicity of

all-silica zeolites in the presence of H2S, the adsorption of binary H2S/H2O mixtures is

investigated.



3.2.1 Molecular Models

All force fields used in this work are non-polarizable and have a rigid geometry. Non-

bonded interactions are modeled using pairwise-additive potentials consisting of Lennard–

Jones (LJ) 12–6 and Coulomb terms:

U(rij) = 4εij

[(σijrij

)12

−(σijrij

)6]

+qiqj

4πε0rij, (3.1)

where rij , εij , σij , qi, and qj are the site–site separation, LJ well depth, LJ diameter,

and partial charges on beads i and j, respectively. The Transferable Potentials for

Phase Equilibria (TraPPE) force field is used for the zeolites, [36] H2S, [37] and CH4, [35]

whereas water is described using the TIP4P model. [102] In the TraPPE-zeo force field,

LJ interaction sites and partial charges are placed on both silicon and oxygen atoms.

H2S is represented by the recently developed 4-site TraPPE model where LJ sites are

placed on the S and H atoms and partial charges are placed on H atoms and an off-

atom site. [37] CH4 is represented by the 5-site TraPPE–EH model where LJ interaction

sites are located at the carbon atom and the four C–H bond centers. [35] The TIP4P

model represents water by a single LJ site on the oxygen atom and partial charges are

placed on H atoms and an off-center site. The standard Lorentz–Berthelot combining

rules [56] are used to determine the LJ parameters for all unlike interactions. Analytical

tail corrections and the Ewald summation method (see below) are applied to account

for the long-range interactions. [60]

3.2.2 Simulation Details

Configurational-bias Monte Carlo simulations [32,59] in the isobaric–isothermal (NpT )

version of the Gibbs ensemble [31,40,57] are used to compute pure (H2S and CH4) and

binary (H2S/CH4 and H2S/H2O) adsorption isotherms in all-silica frameworks at T =

298 and 343 K and p ≤ 50 bar, and also for the vapor–liquid equilibrium between H2S

and H2O at T = 298 K and p = 1 bar. The osmotic version of the Gibbs ensemble [103–105]

where only the sorbate compounds transfer between reservoir and zeolite phases is used

here for two reasons: (i) it does not require one to determine the chemical potentials


Table 3.1: Zeolite unit cell parameters and simulation box sizes used in this work.

Zeolite a b c α β γ Reference Box[Å] [Å] [Å] [deg] [deg] [deg] [cells]

CHA 13.5292 13.5295 14.748 90.00 90.00 120.00 Díaz-Cabañas et al. [106] 3 x 3 x 3DDR 13.860 13.860 40.891 90.00 90.00 120.00 Gies [107] 3 x 3 x 1FER 18.7202 14.0702 7.4197 90.00 90.00 90.00 Morris et al. [108] 2 x 3 x 4IFR 18.496 13.4406 7.7111 90.00 101.58 90.00 Barrett et al. [109] 2 x 3 x 5MFI 20.022 19.899 13.383 90.00 90.00 90.00 Van Koningsveld et al. [110] 2 x 2 x 3MOR 18.11 20.53 7.528 90.00 90.00 90.00 Gramlich [111] 2 x 2 x 4MWW 14.2081 14.2081 24.945 90.00 90.00 120.00 Camblor et al. [112] 3 x 3 x 2

for the selected molecular models in compressed gas or liquid solution phases from a

pre-simulation, and (ii) it more closely resembles the experimental set-up. A system size

of 500 molecules in total is used for all unary and binary simulations probing adsorption

from a gas phase, whereas a total of 1000 molecules is used for probing the adsorption

from a liquid-phase H2S/H2O mixture and also for the vapor–liquid equilibrium of this

mixture. For the zeolite phase, the number of unit cells in each dimension is chosen

to yield a simulation box sufficiently large to encompass a sphere with a diameter of

28 Å. The unit cell dimensions and the number of unit cells in each direction for the

different zeolite frameworks studied here are listed in Table 3.1. With the exception

of MOR, all framework structures studied in this work are available in their all-silica

form. Aluminum atoms in the MOR crystal structure are replaced by silicon atoms

at the same positions for the purpose of this work. The zeolite framework is treated

to be rigid during the course of the simulation, with Si and O atoms fixed at their

crystallographically-determined positions.

The LJ potentials for the sorbate–sorbate interactions in the zeolite and liquid phases

are truncated at 14 Å, whereas the cutoff distance is set to approximately 40% of the

box length for the vapor phase (to achieve a computationally efficient balance between

direct and reciprocal space parts of the Ewald summation). Analytical tail corrections to

energy and pressure are applied for the sorbate–sorbate LJ interactions in all phases. [60]

The Ewald summation method with a screening parameter of κ = 3.2/rcut and an up-

per bound of the reciprocal space summation at Kmax = int(κLbox) + 1 is used for

the calculation of the Coulomb energy. [60] In order to improve the simulation efficiency,


all sorbate–sorbent LJ and Coulomb interactions (using periodic lattice sums to con-

vergence) are pretabulated with a grid spacing of ≈ 0.2 Å and interpolated during the

simulation for any position of an interaction site belonging to a sorbate molecule. [30,113]

Four different types of Monte Carlo moves, including translational, rotational, volume

exchange (only applied between explicitly modeled reservoir phase and ideal gas bath

and not for the zeolite phase), and particle transfer moves, are used to sample the

statistical-mechanical phase space. The coupled–decoupled configurational-bias Monte

Carlo algorithm [59] with the dual cut-off approach [114] is used to enhance the acceptance

rate for particle transfer moves. The probabilities for volume and transfer moves are

adjusted to have approximately one accepted move per Monte Carlo cycle (MCC), [58]

where an MCC consists of a number of randomly selected moves that is equal to the total

number of molecules in the system. In case of binary mixtures, the probability to choose

a molecule type for transfer move is set to allow the ratio of accepted transfers for the

two molecule types to be approximately proportional to the overall composition. The

remaining moves are divided equally between translations and rotations. Production

periods consisting of 25,000 to 50,000 MCCs are used to obtain the unary adsorption

isotherms for CH4 and H2S, while 150,000 MCCs are used for the binary simulations

in order to obtain better statistics even for the dilute compositions. 400,000 MCCs are

used for the adsorption simulations from an extremely dilute liquid phase containing

trace amounts of H2S in H2O. 150,000 MCCs are used for simulating the vapor–liquid

equilibrium of the H2S/H2O mixture.

For binary mixtures, the partial molar enthalpies of adsorption for the two com-

ponents can be quite different and can provide greater insight than simply the overall

enthalpy of adsorption. These are computed from the differences between the total

adsorption enthalpies of configurations that differ in the number of only one species.

For all adsorption systems investigated in this work, eight independent Monte Carlo

simulations are carried out and the statistical uncertainties reported in the following

sections correspond to the standard error of the mean calculated from these independent

simulations.


10-3

10-2

10-1

100

101

102

p [bar]

0.0

0.6

1.2

1.8

2.4

qC

H4

[mm

ol/g

]

0.0

1.0

2.0

3.0

4.0

5.0

qH

2S [

mm

ol/g

]

CHA (298)

CHA (298)

FER (298)

MFI (298)

MOR (298)

MWW (298)

MFI (343)

Figure 3.1: Unary adsorption isotherms for H2S (top) and CH4 (bottom) in differentzeolite framework types. The filled symbols show the experimental data of Maghsoudiet al. [115] for CHA. The legend denotes framework type and temperature in Kelvin. Thestatistical uncertainties are smaller than symbol size.


3.3.1 Unary Adsorption

The adsorption of H2S in an all-silica zeolite was investigated experimentally for the first

time in 2013 by Maghsoudi et al. [115] for the CHA-type framework. To our knowledge,

this is the only available experimental data for H2S adsorption in any crystalline all-

silica material. Figure 3.1 shows the unary adsorption isotherms for H2S and CH4 in the

CHA, FER, MFI, MOR, and MWW frameworks. The saturated vapor pressure of H2S

is 20 and 53 bar at T = 298 and 343 K, respectively. [37,70] In the present work, the focus


Table 3.2: Calculated Henry’s constants for hydrogen sulfide and methane in all-silicazeolites.

Zeolite T HH2S HCH4

HH2S

HCH4

[K][

mmolg·bar

] [mmolg·bar

]CHA 298 8.184 0.7025 11.71

FER 298 21.74 1.241 181

MFI 298 9.81 0.601 16.34

343 2.262 0.2191 10.31

MOR 298 16.875 0.4253 39.74

MWW 298 11.32 0.611 191

is on gas-phase adsorption and, hence, H2S adsorption isotherms are computed only up

to 10 bar at 298 K and up to 50 bar at 343 K. At T = 298 K, there is practically no

adsorption of H2S below p < 10−3 bar, while CH4 does not adsorb appreciably below

0.1 bar. This difference of about two orders of magnitude in the onset pressures for H2S

and CH4 adsorption and the fact that 50% of the H2S saturation capacity is reached for

all five frameworks at p < 1 bar and T = 298 K suggest a fairly high potential for the

separation of these two compounds using all-silica zeolites.

In the low pressure zone, loading is largely determined by the strength of the sorbate–

sorbent interactions. At T = 298 K, FER exhibits the highest loadings at low pressures,

and it can be inferred that both H2S and CH4 bind more strongly to the FER-type

framework. This is also reflected in the Henry’s constants, HH2S and HCH4 , that are

summarized in Table 3.2. As zero loading is approached, the Henry’s constant helps to

quantify the extent of adsorption of a particular species in a particular framework at a

given fugacity (approximated by pressure for near-atmospheric conditions). The ratio of

the Henry’s constants of two species is a good metric to quantify their binary selectivity

at low loadings. As can be seen from Table 3.2, MOR has the highest selectivity towards

H2S while CHA is the least selective. As illustrated by the data in Figure 3.1, the

adsorption capacities, which depend on the accessible pore volume for a framework

type, are also quite different; CHA and MWW exhibit much higher values of loading

near saturation than those found for FER, MFI, and MOR.

As can be seen from the adsorption isotherms for CHA, there is a very good agreement


0 0.25 0.5 0.75y

H2S

8

16

24

32

40

48

αH

2S

FER (298, 1)

FER (298, 10)

FER (343, 1)

FER (343, 10)

FER (343, 50)

0 0.25 0.5 0.75y

H2S

MFI (298, 1)

MFI (298, 10)

MFI (343, 1)

MFI (343, 10)

MFI (343, 50)

0 0.25 0.5 0.75 1y

H2S

CHA (298, 1)

DDR (298, 1)

IFR (298, 1)

MOR (298, 1)

MOR (298, 10)

MWW (298, 1)

Figure 3.2: H2S versus CH4 selectivity as a function of vapor-phase composition. Thelegend denotes framework type, temperature in Kelvin, and total pressure in bar. Thestatistical uncertainties are smaller than the symbol size.

between the experimental and simulation data for both H2S and CH4. Together with

the fact that the TraPPE force field describes the interactions between CH4 and H2S

very accurately, as judged from the binary vapor–liquid equilibria for H2S/CH4, [37] this

suggests that binary simulations using the TraPPE force field for these molecules in

all-silica zeolites should provide accurate estimates for binary loadings and selectivities.

3.3.2 Binary Adsorption of H2S/CH4 Mixtures

In gas reservoirs, natural gas exists in a considerable variety of compositions; especially,

the sourness of the gas stream can vary from a few ppm of H2S to as high as 90 vol%

in some cases. [42] Hence, to design processes for natural gas sweetening, it is of value

to understand the adsorption behavior over a wide range of H2S mole fractions. Binary

adsorption selectivities of H2S over CH4 in different zeolite frameworks at varying gas-

phase compositions, overall pressures, and temperatures are presented in Figure 3.2.

The selectivity is defined here as a measure of the enrichment gained at equilibrium by


contacting a gas mixture with the zeolite,

αH2S =xH2S/xCH4

yH2S/yCH4

, (3.2)

where xH2S and xCH4 are mole fractions in the adsorbed phase, and yH2S and yCH4

are mole fractions in the gas phase. At T = 298 K and 1 bar total pressure, the

selectivities range from a value of 12.2 for DDR at yH2S = 0.007 to 44.4 for MOR

at yH2S = 0.004. For all temperature/pressure combinations, the simulation data show

that the composition dependencies of the selectivity for preferential H2S adsorption vary

significantly for different zeolites. At T = 298 K and 1 bar total pressure, the selectivity

nearly doubles for MFI when the H2S gas-phase concentration is changed from very

dilute to about 90 mol%, increases by a factor of 1.6 for CHA, 1.4 for DDR, 1.3 for IFR,

1.2 for FER and MWW, and decreases by close to a factor of 2 for MOR. The peculiar

behavior for MOR is due to a few highly selective adsorption sites that are exhausted

beyond a certain H2S loading, and this leads to a sharp fall in selectivity. At T = 298 K

and 1 bar total pressure, MOR exhibits the highest selectivity up to about 35 mol% H2S

in the gas phase, beyond this concentration MFI yields the highest selectivity. At 10 bar

overall pressure, this switchover between the most selective zeolite happens at lower H2S

concentration, below 10 mol%. Once again, this shift can be explained by the limited

number of very favorable sites in MOR that get filled at lower concentration when the

total pressure is higher. A very encouraging result for the application of all-silica zeolites

for natural gas sweetening is that the selectivities in FER and MFI increase as the total

pressure increases from 1 to 10 bar at both T = 298 and 343 K.

It is clear from Figure 3.2 that the selectivity is strongly affected by changes in the

temperature. For FER, the selectivity decreases by a factor of 1.8 as T is increased

from 298 to 343 K, and the decrease is close to a factor of 2.3 and 2.0 for MFI at a

total pressure of 1 and 10 bar. At the lower temperature (298 K), enthalpic factors

due to the different interactions of H2S and CH4 with the zeolite framework play a

larger role for determining the selectivity. At the higher temperature (343 K), entropic

contributions become more important, and differences in the strengths of interactions

with the adsorbent play a smaller role for determining selectivities. This issue will be

revisited when discussing the partial molar enthalpies of adsorption at different state


0 0.8 1.6 2.4q

H2S [mmol/g]

8

16

24

32

40

48

αH

2S

FER (298, 1)

FER (298, 10)

FER (343, 1)

FER (343, 10)

FER (343, 50)

0 0.8 1.6 2.4q

H2S [mmol/g]

MFI (298, 1)

MFI (298, 10)

MFI (343, 1)

MFI (343, 10)

MFI (343, 50)

0 0.8 1.6 2.4 3.2q

H2S [mmol/g]

CHA (298, 1)

DDR (298, 1)

IFR (298, 1)

MOR (298, 1)

MOR (298, 10)

MWW (298, 1)

Figure 3.3: H2S versus CH4 selectivity as a function of H2S loading. The legend de-notes framework type, temperature in Kelvin, and total pressure in bar. The statisticaluncertainties are smaller than the symbol size.

points.

For selecting higher performing zeolites for natural gas sweetening from all candidate

structures, in addition to the binary selectivity, it is also important for these zeolites

to provide higher loading levels. The dependence of the selectivity on H2S loading is

depicted in Figure 3.3. It can be seen that the selectivity curves for different overall

pressures, but for a given framework type and temperature, nearly collapse onto one

another. This implies that at a given temperature, the selectivity is mainly dependent

on the H2S loading. MFI is found to possess the highest selectivity at loadings above

≈ 1.6 mmol/g, whereas MOR shows a much higher selectivity at lower qH2S. In general,

the selectivities are found to increase with qH2S. The exceptions are MOR, where the

number of highly favorable H2S adsorption sizes is limited and a minimum is observerd

at qH2S ≈ 2.2 mmol/g that is followed by the usual increase in selectivity, and FER and

MFI at T = 343 K and a total pressure of 50 bar (and less pronounced for FER at

T = 298 K and p = 10 bar), where a maximum is found near saturation loading. This

latter feature will be discussed further below.

Figure 3.4 shows the spatial distribution of CH4 and H2S in MFI and MOR at


Figure 3.4: Number density distribution (in units of Å−3) for H2S (left) and CH4 (right)at T = 298 K, p = 10 bar: (a) yH2S = 0.015 in MFI, (b) yH2S = 0.51 in MFI, (c)yH2S = 0.015 in MOR, and (d) yH2S = 0.47 in MOR. The number densities are shownin the ab-plane for the entire simulation box with the number of units cells provided inTable 3.1 and averaged along the c-axis. For MOR, the small pores are located in thedense region of the framework and yield sharp density enhancements, whereas the large12-membered ring channels along the c-axis yield more diffuse density enhancements.


T = 298 K and p = 10 bar for equilibrium gas-phase compositions low and high in

H2S (yH2S ≈ 0.015 and ≈ 0.5, respectively). At this state point, the loadings for unary

adsorption of H2S are 3.1 and 3.0 mmol/g in MFI and MOR, respectively, and 1.9 and

1.7 mmol/g for CH4 in MFI and MOR, respectively. These values correspond to about

90 and 50% of the saturation loading for H2S and CH4, respectively. In MFI, straight

channels along the b-direction and sinusoidal channels along the a-direction form in-

tersections that provide a larger free volume than the channels. Both types of sorbate

molecules exhibit a modest preference to adsorb near the mouth of the sinusoidal chan-

nels, but also near the center of the straight channels and in the low-curvature segments

of the sinusoidal channels. At yH2S = 0.015, H2S molecules are found throughout the

entire two-dimensional channel system of MFI, whereas CH4 is almost entirely displaced

at yH2S = 0.51 and is found only in the intersections. Note that unary adsorption of

CH4 at low pressure yields a preference for channel locations in agreement with previous

simulations. [113]

The density distributions in MOR differ markedly from those found in MFI. In MOR,

both compounds exhibit a very strong preference for adsorption in the smaller pores that

are confined by 4- and 8-membered rings. At yH2S = 0.015, the densities for H2S and

CH4 are similar in these smaller pores, whereas a larger amount of CH4 is adsorbed

in the larger pores formed by 12-membered rings. Thus, H2S displaces CH4 from the

most favorable sites. At yH2S = 0.47, the density of CH4 in the smaller pores becomes

negligible and these pores are almost exclusively filled by H2S molecules (the densities

differ by more than two orders of magnitude). In the larger MOR pores, there is a slight

preference to locate closer toward the walls parallel to the b-axis and the H2S density

exceeds that for CH4 by a factor of ≈ 15 at yH2S = 0.47.

Snapshots of the adsorbed phases (T = 298 K, p = 1 bar, and yH2S ≈ 0.05) in all

framework types investigated here and a brief description of the adsorption sites are

provided in the Supporting Information.1

In addition to the capacity and selectivity of an adsorbent toward the desired com-

ponent, there are a few other attributes that also play a role in determining the optimal1https://pubs.acs.org/doi/suppl/10.1021/acs.langmuir.5b03015/suppl_file/la5b03015_si_

001.pdf

https://pubs.acs.org/doi/suppl/10.1021/acs.langmuir.5b03015/suppl_file/la5b03015_si_001.pdf

https://pubs.acs.org/doi/suppl/10.1021/acs.langmuir.5b03015/suppl_file/la5b03015_si_001.pdf


adsorbent for a given application. Among these factors, the enthalpy of adsorption is ex-

tremely important because it determines the heating and cooling duties and, hence, to a

large extent the operating cost of an adsorption unit. Figure 3.5 shows the partial molar

enthalpies of adsorption, ∆Hads, for H2S and CH4 as function of H2S loading computed

from binary adsorption simulations. Enthalpies of adsorption for both compounds in

the majority of zeolites, with MOR and MWW being the exceptions, become increas-

ingly more favorable (larger in magnitude) with increasing H2S loading. The ∆Hads

values include contributions from interactions of the sorbate with the bare framework

and with other sorbate molecules. In general, as loading decreases, sorbate molecules

are able to find sites providing more favorable interactions with the framework, i.e.,

the contribution of sorbate–sorbent interactions can only cause a decrease in |∆Hads|with increasing loading (see Figure 6 in the Supporting Information). Therefore, the

increase in |∆Hads| with qH2S must be a result of favorable interactions with guest H2S

molecules (see Figure 7 in the Supporting Information). The increase of |∆Hads| withqH2S is largest (≈ 20%) for CHA, the zeolite with the highest saturation loading and a

relatively constant sorbate–sorbent interaction energy.

For MOR, the adsorption entalpies for both H2S and CH4 are most favorable for gas

streams very dilute in H2S. As qH2S increases, |∆Hads| decreases for both H2S and CH4,

but the absolute change in |∆Hads| is significantly larger for H2S than for CH4. That

is, the adsorption enthalpies mirror the trend of decreasing selectivity with increasing

qH2S. The reason for this behavior is the strong preference to adsorb in the smaller

pores of MOR (see Figure 3.4). The |∆Hads| values for H2S at low qH2S are about

2 kJ/mol smaller at p = 10 bar than those at p = 1 bar because the higher pressure

reduces the availability of the small pores for H2S due to more of them being occupied

by CH4. The adsorption enthalpies reach a maximum at qH2S ≈ 2.2 mmol/g for H2S and

qH2S ≈ 1.6 mmol/g for CH4. At this point favorable sorbate–sorbate interactions are able

to overcome the decrease of favorable sorbate–sorbent interactions caused by the limited

availability of smaller pores in MOR. Adsorption in the MWW framework constitutes an

intermediate case, where a decrease of favorable sorbate–sorbent interactions is balanced

by an increase in favorable sorbate–sorbate interactions. As a result, ∆Hads for both

compounds and αH2S (see Figure 3.3) do not change appreciably over a wide range of

qH2S.


0 0.8 1.6 2.4q

H2S [mmol/g]

-36

-32

-28

-24

-20

-16

∆H

ad

s [kJ/m

ol]

FER (298, 1)

FER (298, 10)

FER (343, 1)

FER (343, 10)

FER (343, 50)

0 0.8 1.6 2.4q

H2S [mmol/g]

MFI (298, 1)

MFI (298, 10)

MFI (343, 1)

MFI (343, 10)

MFI (343, 50)

0 0.8 1.6 2.4 3.2q

H2S [mmol/g]

MOR (298, 1)

MOR (298, 10)

MWW (298, 1)

CHA (298, 1)

DDR (298, 1)

IFR (298, 1)

Figure 3.5: Partial molar enthalpies of adsorption of H2S (larger |∆Hads|) and CH4

(smaller |∆Hads|) as a function of H2S loading from binary mixtures of various compo-sitions. The legend denotes framework type, temperature in Kelvin, and total pressurein bar.

The adsorption selectivity reflects the difference of the Gibbs free energies of transfer

of the two sorbate molecules from the vapor phase to the zeolite. The Gibbs free energy

can be separated into enthalpic and entropic terms. Figure 3.6 depicts the adsorption

selectivity for H2S over CH4 as function of the difference in adsorption enthalpies. With

the exception of the data for FER and MFI at T = 343 K and p = 50 bar, αH2S values

are linearly correlated with ∆∆Hads. Thus, changes in the adsorption enthalpies govern

changes in the selectivity. At low qH2S, ∆∆Hads ≈ 6 kBT for MOR and αH2S > 40 is

achieved. In contrast, the ∆∆Hads values for the other zeolites fall into the range from

3 to 4 kBT and the selectivities fall into the range from 12 to 22. For FER and MFI,

the data at p = 1 and 10 bar nearly coincide; an indication that entropic effects due to

pore crowding are not significant for this pressure range. In contrast, crowding of the

smaller pores is important for adsorption in MOR and, for a given ∆∆Hads value, the

selectivity is larger at p = 10 bar because the entropic penalty for CH4 to reside in the

smaller pores is larger than at p = 1 bar.

As shown in Figures 3.2 and 3.3, the zeolite frameworks FER and MFI exhibit a


2 3 4∆∆H

ads / k

BT

10

20

30

40

50

αH

2S

FER (298, 1)

FER (298, 10)

FER (343, 1)

FER (343, 10)

FER (343, 50)

2 3 4∆∆H

ads / k

BT

MFI (298, 1)

MFI (298, 10)

MFI (343, 1)

MFI (343, 10)

MFI (343, 50)

3 4 5 6 7∆∆H

ads / k

BT

CHA (298, 1)

DDR (298, 1)

IFR (298, 1)

MOR (298, 1)

MOR (298, 10)

MWW (298, 1)

Figure 3.6: H2S versus CH4 selectivity (on logarithmic scale) as function of the differencein adsorption enthalpies of CH4 and H2S. The legend denotes framework type, temper-ature in Kelvin, and total pressure in bar. The statistical uncertainties are smaller thanthe symbol size.

significant decrease in the selectivity for H2S over CH4 as the temperature is increased

from 298 to 343 K. For FER, the change in temperature does not affect the ∆Hads values

for both compounds to any significant extent (see Figure 3.5). In contrast, for MFI, the

shift in ∆Hads is larger for H2S than for CH4 and ∆∆Hads is increased by ≈ 0.5 kJ/mol.

Nevertheless, the distribution of the sorbate molecules is not altered appreciably by the

temperature increase, and the main reason for the decrease in selectivity is the increased

importance of entropic factors that disfavor preferential adsorption of H2S.

An interesting feature observed for these binary mixtures is the maximum in the

adsorption selectivity at T = 343 K and p = 50 bar for the FER and MFI frameworks

(see Figures 3.2 and 3.3), which is reflected in the very non-linear behavior of the αH2S

versus ∆∆Hads correlation (see Figure 3.6). A possible explanation would be that the

pore architecture limits the number of sorbate–sorbate contacts. Figure 3.7 shows the

loading dependence of the number of H2S neighbors in the first solvation shell of H2S.

The sorbate packings differ significantly between FER and MFI with the latter allowing

about twice as many molecules in the solvation shell at a given loading. Nevertheless, the


0.0

0.6

1.2

1.8

2.4

3.0

Nin

tzeo

0 0.8 1.6 2.4 3.2q

H2S [mmol/g]

0.0

0.3

0.6

0.9

Nin

tgas

FER (343, 10)

FER (343, 50)

MFI (343, 10)

MFI (343, 50)

Figure 3.7: Number of [S]H2S–[S]H2S neighbors within the first solvation shell (rS−S ≤5.4 Å) in the zeolite (top) and the corresponding gas phase (bottom) at T = 343 K andp = 10 and 50 bar. The legend denotes framework type, temperature in Kelvin, andtotal pressure in bar. The statistical uncertainties are smaller than the symbol size.

number of nearest neighbors are linearly correlated with the loading in both frameworks

and there is no indication of a decrease in the slope at higher loading. At the qH2S values

corresponding to the maximum in αH2S (qH2S > 2.2 mmol/g for FER and > 2.6 mmol/g

for MFI), the H2S adsorption isotherms reach their flat region as the saturation loading

is approached. Calculation of the partial molar sorbate–sorbate energy of adsorption (see

Figure 7 in the Supporting Information) indicates a change in the slope as saturation


26 28 30 32 34 36|∆H

ads| [kJ/mol]

8

16

24

32

40

48

αH

2S

CHAFERMFIMORMWWDDRIFR

Figure 3.8: H2S versus CH4 selectivity as function of |∆Hads| for H2S at T = 298 K andp = 1 bar. The statistical uncertainties are smaller than the symbol size.

loading is approached. The reason for this change in slope is not so much that sorbate–

sorbate interactions in the zeolite phase become less favorable, but a significant increase

in sorbate–sorbate interactions in the H2S-rich gas phase as indicated by an exponential

increase of the number of neighbors in the first solvation shell (see Figure 3.7).

A large αH2S value requires a large ∆∆Hads value which in turn requires a large

|∆Hads| for H2S. With respect to the heating and cooling duties for sorption-based sepa-

rations, however, one would like a sorbent that for a given |∆HH2Sads | yields a higher αH2S

(or for a given αH2S requires a smaller |∆HH2Sads |). The data in Figure 3.8 demonstrate

significant variations that can be exploited for finding an optimal sorbent material. For

example, for |∆HH2Sads | ≈ 32 kJ/mol, αH2S values of ≈ 22, 27, and 34 are found for the

FER, MFI, and MOR frameworks, and αH2S ≈ 24 requires |∆HH2Sads | ≈ 33, 31, and

28 kJ/mol for these three zeolites. That is, one may achieve an increase in αH2S by

50% or a decrease in |∆HH2Sads | by 20% by judicious choice of the framework. Overall,

the data for MOR are found closest to the upper left corner of Figure 3.8 indicating

that this framework may be optimal under many conditions, whereas the data for CHA,


DDR, and FER fall closest to the lower right corner. However, these data do not reflect

the different trends with increasing loading that are observed for MOR compared to the

other frameworks (see Figure 3.3).

3.3.3 Assessment of Ideal Adsorbed Solution Theory

Experimental measurements of multi-component adsorption isotherms with a high de-

gree of accuracy and precision still remain a challenge, whereas unary adsorption mea-

surements are comparably easy to carry out. Thus, numerous approaches have been

suggested to predict mixture adsorption from the knowledge of pure-component adsorp-

tion isotherms. [98] The most widely used approach, called ideal adsorbed solution theory

(IAST), was proposed by Myers and Prausnitz in 1965. [116] IAST treats the adsorbed

phase akin to a liquid by using equations analogous to the thermodynamics for multi-

component vapor–liquid equilibria. IAST is thermodynamically consistent and also quite

easy to apply. The adsorption selectivity is defined analogous to the inverse of the rela-

tive volatility. Under conditions where Raoult’s law is applicable, the relative volatility

is simply equal to the ratio of the pure-component vapor pressures at the temperature

of interest,

αRLVLE =

psat1

psat2

, (3.3)

and, hence, the separation factor for binary vapor–liquid equilibria is independent of

composition. For binary adsorption, this separation factor is defined as: [116]

αIASTads =

p02(π)

p01(π)

, (3.4)

where p0i (π) is the equilibrium gas-phase pressure corresponding to the solution spread-

ing pressure, π, for the adsorption of pure component i. Since π can be a function

of adsorbed-phase composition and loading, contrary to ideal vapor–liquid equilibria,

αIASTads can vary with the fluid-phase composition. The dependence of the separation

factor on the gas-phase composition is determined by the shapes and locations of the

single-component adsorption isotherms for the species constituting the multi-component

mixture. [116]

In Figure 3.9, qH2S and qCH4 obtained directly from simulations for binary mixtures


0

0.8

1.6

2.4

3.2

q [

mm

ol/g

]

10-3

10-2

10-1

100

pH

2S [bar]

0

0.8

1.6

2.4

q [

mm

ol/g

]

10-3

10-2

10-1

100

pH

2S [bar]

10-3

10-2

10-1

100

101

102

pH

2S [bar]

a) CHA (298 K) b) FER (298 K) c) MFI (298 K)

d) MOR (298 K) e) MWW (298 K) f) MFI (343 K)

Figure 3.9: Comparison of H2S and CH4 loadings from binary simulations and predictedusing IAST as function of partial pressure. Data for H2S obtained from binary simula-tions are represented by red, green, and magenta squares for overall pressures of 1, 10,and 50 bar, respectively. Data for CH4 obtained from binary simulations are representedby blue, black, and violet circles for overall pressures of 1, 10, and 50 bar, respectively.The lines of the same colors denote the H2S and CH4 loadings obtained from IAST.Framework type and temperature are indicated for each sub-figure.

and predicted using IAST (with input from simulations for unary systems) are com-

pared for five different zeolite frameworks (CHA, FER, MFI, MOR, and MWW). The

data indicate that there is very good agreement for the overall shape of the adsorption

isotherms and near quantitative agreement for the loading of the species found in higher

concentration in the zeolite phase. Such an agreement between IAST predictions and

binary measurements indicates that (i) there are no adsorption sites that are inaccessible

to either CH4 or to H2S in any of the investigated zeolites (both molecules are mostly

spherical and have very similar sizes) and (ii) that the interactions between adsorbates

are smaller in magnitude than the sorbate–sorbent interactions.

The absolute scale used in Figure 3.9 hides to some extent the deviations that are


0.8

1.0

1.2

1.4

1.6

qIA

ST/q

bin

ary

0 0.8 1.6 2.4q

H2S [mmol/g]

0.6

0.8

1.0

1.2

qIA

ST/q

bin

ary

0 0.8 1.6 2.4q

H2S [mmol/g]

0 0.8 1.6 2.4 3.2q

H2S [mmol/g]

a) CHA (298 K) b) FER (298 K) c) MFI (298 K)

d) MOR (298 K) e) MWW (298 K) f) MFI (343 K)

Figure 3.10: Ratio of loadings predicted using IAST and obtained directly from simula-tions for binary mixtures. Data for H2S are shown as red squares, orange up triangles,and magenta circles for p = 1, 10, and 50 bar, respectively. Data for CH4 are shownas blue diamonds, cyan down triangles, and violet crosses for p = 1, 10, and 50 bar,respectively. Framework type and temperature are indicated for each sub-figure.

found for compositions where one component is only sparingly adsorbed. Relative data

(see Figure 3.10) provide a better assessment of IAST’s shortcomings for the systems

investigated in this work. With the exception of the data for MOR at higher pressure,

IAST overpredicts qH2S for reservoir phases dilute in H2S, and the extent of the overpre-

diction is ≈ 40% for CHA, MFI, and MWW at T = 298 K. The underestimation of qH2S

for MOR at T = 298 K and p = 10 bar is likely caused by the competition for the smaller

pores (see Figure 3.4). In addition, IAST is found to unpredict qCH4 at intermediate

qH2S where IAST does not reflect the significant effects of H2S co-adsorption. For MOR,

qCH4 is underestimated by up to a factor of 1.6.

A comparison of the selectivities predicted from IAST versus those determined from

binary simulations is illustrated in Figure 3.11. Although IAST predicts correctly that

MOR exhibits the highest αH2S values for low yH2S and that αH2S values increase with

increasing yH2S (with the exception of MOR), IAST yields deviations of more than 10%


0 0.25 0.5 0.75 1y

H2S

0.8

1.0

1.2

1.4

1.6

CHA (298, 1)

FER (298, 1)

FER (298, 10)

MOR (298, 1)

MOR (298, 10)

MWW (298, 1)

0 0.25 0.5 0.75 1y

H2S

0.8

1.0

1.2

1.4

1.6

αIA

ST/α

bin

ary

MFI (298, 1)

MFI (298, 10)

MFI (343, 1)

MFI (343, 10)

MFI (343, 50)

Figure 3.11: Ratio of adsorption selectivities predicted using IAST and obtained directlyfrom binary simulations as function of gas-phase mole fraction. The legend denotesframework type, temperature in Kelvin, and total pressure in bar.

for about half of the data points. In the low H2S mole fraction regime, IAST overpredicts

αH2S for MFI, CHA, FER, and MWW by 10 to 40%, and the αIAST/αbinary values

decrease with increasing yH2S. For MOR at T = 298 K and p = 1 bar, the deviation

is about 10% at low yH2S, but increases with yH2S and reaches values in excess of 50%

at high yH2S. Overall, application of IAST holds some promise for the initial screening

of zeolites for natural gas sweetening, but its margin of error is too large to rely on it

to distinguish better performing zeolites, and extensive computations/measurements of

multi-component adsorption remain necessary.


3.3.4 Binary Adsorption of H2S/H2O Mixtures

The synthesis of silicalite, a silica polymorph with the MFI framework, by Flanigen

and Patton [117] was a remarkable milestone in the history of zeolite synthesis. They

introduced the use of fluoride anions as mineralizers instead of the conventional hydrox-

ide anions. This enabled a low-pH synthesis that greatly reduces the extent of silanol

(Si–OH) defects by condensation of adjacent groups. The fluoride ions also serve as sub-

stitutes for the siloxy ions (Si–O−) to neutralize the cationic structure-directing agents,

and in turn reduce these defects. As a result, Flanigan and Patton were successful in

synthesizing a highly defect-free silica material that is extremely hydrophobic. The all-

silica analogues of zeolites are very good candidates for separations requiring the selective

exclusion of water. However, this will only be possible if water is not entrained into the

zeolite by the species that are the target of the adsorption. For example, the adsorption

of ethanol or other hydrogen-bonding compounds induces significant co-adsorption of

water. [105,118]

In order to investigate whether the assumption about hydrophobicity holds true for

natural gas sweetening with all-silica zeolites, the binary H2S/H2O adsorption is studied

in MFI at T = 298 K and p = 1 bar. MFI is chosen because of its availability in

the nearly defect-free silicalite form and because it exhibits the highest αH2S at higher

qH2S for the binary H2S/CH4 mixture (see Figure 3.3). At the selected state point,

the H2S/H2O mixture exists as a two-phase system with a very low H2S solubility in

the liquid phase and a very low partial pressure of H2O in the vapor phase. In order

to avoid computing adsorption selectivities in the large part of the composition range

that falls into the vapor–liquid coexistence region, the coexistence compositions are

determined here as a first step. Subsequent adsorption simulations are carried out at

four different fluid-phase compositions (two in the one-phase vapor region and another

two in the one-phase liquid region). The simulation data are listed in Table 3.3, where

the selectivity is given by α12H2S = (x1

H2S/x1H2O)/(x2

H2S/x2H2O). For the vapor–liquid

equilibrium, the simulations yield α12H2S = 46000. This value is ≈ 2.7 times larger than

the corresponding experimental value, [119] because use of non-polarizable models leads

to an underestimation of the H2S concentration in the liquid phase.

For adsorption from the vapor phase, the selectivity for H2S over H2O is found to be

18, i.e., only about a factor of 2 smaller than the selectivity for H2S over CH4 at similarly


Table 3.3: Compositions and selectivities for vapor–liquid and adsorption equilibria inMFI calculated for the binary H2S/H2O mixture at T = 298 K and p = 1 bar.

phase 1 phase 2 x1H2S x2

H2S α12H2S

vapor liquid 0.9511 0.000421 4.62 ∗ 104

zeolite vapor 0.99831 0.96971 181

0.99721 0.95471 171

zeolite liquid 0.98643 0.0000804 916 ∗ 104

0.9681 0.0000351 863 ∗ 104

high H2S concentrations in the gas phase. A selectivity of 18 is more than sufficient

to allow for the use of all-silica MFI for the sweetening of moisture-laden natural gas

streams. At first glance, it might appear that MFI is exceedingly hydrophobic when

adsorption occurs from the liquid phase, but this difference is entirely due to the large

relative volatility of H2S in binary H2S/H2O mixtures. That is, when the selectivity for

adsorption from the liquid phase is divided by the relative volatility, then one obtains a

value that within statistical uncertainites agrees with the selectivity for adsorption from

the gas phase ((91 + 86) ∗ 104/2 ∗ 4.6 ∗ 104 = 19).

3.4 Conclusions

Adsorption of H2S and CH4 in seven different all-silica zeolite frameworks is probed over

a wide range of H2S partial pressures. Although all of the investigated frameworks are

of the all-silica form, there is a considerable variation in selectivity toward H2S that

falls into the range from 12 for DDR to 44 for MOR at yH2S < 0.007, T = 298 K, and

p = 1 bar. At low H2S equilibrium concentrations in the vapor phase (below ≈ 10% but

depending on the phase ratio, the initial feed concentration could be significantly higher),

MOR has the highest selectivity and also the most favorable enthalpy of adsorption for

H2S due to very favorable sorbate–sorbent interactions in its smaller pores. At high

H2S equilibrium concentrations, MFI exhibits the highest selectivity and also the most

favorable enthalpy of adsorption for H2S due to favorable sorbate–sorbate interactions.

The precise point where the adsorption selectivities in MOR and MFI cross over depends

on temperature and total pressure but, for a given value ot ∆HH2Sads , MOR yields a


larger αH2S. Ideal adsorbed solution theory is found to predict the salient features

for binary H2S/CH4 mixtures, but it lacks the quantitative accuracy to select between

high-performing zeolites. For gas-phase adsorption, silicalite provides a selectivity for

H2S over H2O that approaches 20 and is promising for sour-gas sweetening even in the

presence of moisture.

Chapter 4

Identifying Optimal Zeolitic

Sorbents for Sweetening of Highly

Sour Natural Gas

From M. S. Shah, M. Tsapatsis, and J. I. Siepmann, Angew. Chem. Intl. Ed. 2016, 55,

5938–5942. Copyright c© 2016 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Reprinted by permission of John Wiley & Sons, Inc. https://onlinelibrary.wiley.

com/doi/full/10.1002/ange.201600612

4.1 Introduction

In recent years, discovery of shale gas and advancement in fracking technologies have

led to a large increase in the North American natural gas production. However, even

today, a significant fraction of the global gas reserves continues to remain untapped,

and this is due to the sour nature of these reservoirs with H2S concentrations high

enough to deem the conventional amine-based absorptive separation followed by a Claus

process as uneconomical. [120] Finding innovative and cost-effective solutions for sour gas

sweetening can have far-reaching environmental and economical implications. While

there are several adsorbent materials available for H2S removal under dilute conditions,

the SPREX process [121] using cryogenic distillation is, at present, the only alternative to

63

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Chapter 4: Identifying Optimal Zeolitic Sorbents for Sweetening of Highly Sour NaturalGas 64

amines for bulk H2S removal. For adsorptive separations, one of the main challenges for

selective H2S removal from sour gas is the presence of H2O vapor because H2O, with its

higher dipole, possesses a higher affinity for strong adsorption sites. Selectivity can be

achieved through a chemical reaction, but this leads to an inherently energy-intensive

separation. [122–124] Siliceous zeolites (high Si/Al ratio) containing only minute quantities

of polar cations and silanol defects are known to be very hydrophobic, [41] and offer an

opportunity to selectively capture H2S from moist natural gas. [115,125,126]

In silico discovery of optimal porous materials for gas storage, separations, and catal-

ysis has added a new scientific dimension by not only accelerating materials screening,

but by also providing molecular insights for rational design. [26,27,29,30,127] This approach

becomes specially important for systems involving very hazardous chemicals like H2S,

where the costs and risks associated with experimental measurements for even a small

number of materials are quite high. Advances in efficient Monte Carlo algorithms [31,128]

and accurate force fields [36,37] have enabled predictive modeling of phase and sorption

equilibria. Our goal here is to assess zeolite-based adsorptive processes for sweetening

of sour gas mixtures by a computational screening (see Supporting Information, SI,1 for

a detailed description) of all the 386 electrically neutral structures found in the IZA–SC

database. [25]

Natural gas obtained at the well head varies considerably in composition, temper-

ature, and pressure depending on the geographical location. [42] Sour gas mixtures may

contain not only CH4, H2S, and CO2, but also ethane (C2H6) and other light alkanes

that are even more valuable as fuel and chemical feedstock. [129] Previously, we have

shown that depending upon the strengths of the sorbate–sorbate and sorbate–sorbent

interactions, the H2S/CH4 selectivity, SM, changes differently with feed composition for

different frameworks. [126] Accordingly, in this study, we evaluate performance at three

different H2S mole fractions in the feed (yF = 0.10, 0.30, and 0.50) for binary H2S/CH4

and H2S/C2H6 mixtures. This relatively large composition range reflects that the treat-

ment may involve a multi-stage adsorption unit, and may also be applicable to ultra-sour

natural gas mixtures. We focus discussion on performance at T = 343 K and p = 50 bar,

but we also carry out simulations at 298 K and 10 bar and find a very good correlation1https://onlinelibrary.wiley.com/action/downloadSupplement?doi=10.1002%2Fange.

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between the data at different state points (see SI).


4.2.1 Molecular Models

Non-bonded interactions are modeled using a pairwise-additive potential consisting of

Lennard–Jones (LJ) 12–6 and Coulomb terms:

U(rij) = 4εij

[(σijrij

)12

−(σijrij

)6]

+qiqj

4πε0rij, (4.1)

where rij , εij , σij , qi, qj are the site-site separation, LJ well depth, LJ diameter, and

partial charges on beads i and j, respectively. The Transferable Potentials for Phase

Equilibria (TraPPE) force field is used for the zeolites, H2S, CH4, C2H6, CO2, and N2.

In the TraPPE-zeo force field, [36] LJ interaction sites and partial charges are placed

on both silicon and oxygen atoms. H2S is represented by the recently developed 4-site

TraPPE model where LJ sites are placed on the S and H nuclei and partial charges are

placed on H nuclei and an off-atom site. [37] For CH4, the 5-site TraPPE–EH model where

LJ interaction sites are located at the carbon nucleus and the four C–H bond centers [35]

is used. For C2H6, the 2-site TraPPE–UA model with LJ interaction sites located at

the carbon nuclei, [34] is used to gain a factor of order 10 in efficiency compared to the

8-site TraPPE–EH version. The TraPPE models for CO2 and N2, [55] that account for

the quadrupole moments of these molecules, are used to describe these molecules for

the multi-component mixture simulations. The standard Lorentz–Berthelot combining

rules: [56]

σij =σii + σjj

2and εij =

√εiiεjj , (4.2)

are used to determine the LJ parameters for all unlike interactions.

4.2.2 Simulation Details

Monte Carlo simulations in the isobaric–isothermal (NpT ) version of the Gibbs ensem-

ble [31] are used to compute the binary (H2S/CH4 and H2S/C2H6) adsorption isotherms

in all-silica frameworks at T = 343 K and p = 50 bar and at T = 298 K and


p = 10 bar. At T = 343 K and p = 50 bar, five different overall compositions,

zH2S = 0.10, 0.30, 0.50, 0.70, and 0.90 have been simulated for each zeolite, while only

zH2S = 0.50 has been used for the lower temperature. This wide composition range is

used here to also allow for the study of multi-stage adsorption processes. Note that zH2S

is not equal to yF with the latter corresponding to the feed composition at the inlet of

a breakthrough column. For 16 selected zeolites (names provided in Figure 3), a five-

component mixture of H2S:CO2:CH4:C2H6:N2 with the molar ratio of 25:10:50:10:5 is

simulated at T = 343 K and p = 50 bar. Additionally, another four-component mixture

of H2S:CO2:CH4:C2H6 with the molar ratio of 16:10:70:4 is simulated at T = 343 K

and p = 24 bar (the current pressure of the Lacq gas field). The total number of gas

molecules in the two-phase system is taken to be proportional to the mass of the sim-

ulated zeolite (1 mole gas mixture contacted for every mole of silicon atoms). This

additional constraint and the integer nature of the number of molecules result in overall

compositions that are very close to zH2S, but not exactly zH2S.

The zeolite framework is treated to be rigid during the course of the simulation, with

Si and O atoms fixed at their crystallographically-determined positions. Only those

frameworks in the ISA–SC database that have no net charge remaining in a unit cell

after removing any bound ions or solvent molecules and contain only Si, O, P, and Al

atoms are used for the purpose of this work. The force field parameters for P and Al

are taken to be same as that for Si; this approximation can be justified to some extent

because Al and P are immediate neighbors of Si in the same row of the periodic table,

and are likely to have very similar strength of dispersive interactions.

For the zeolite phase, the number of unit cells in each dimension is chosen to encom-

pass a sphere with a diameter of at least 28 Å and the LJ term and the direct-space

part of the Coulomb interaction are truncated at 14 Å. The cutoff for vapor-phase in-

teractions is set to approximately 40% of the box length. Analytical tail corrections are

applied for the LJ term. The Ewald summation method with screening parameter of

κ = 3.2/rcut and Kmax = int(κLbox) + 1 for the upper bound of the reciprocal space

summation is used for the calculation of first-order electrostatics. [60] In order to improve

the efficiency of simulation, all sorbate–sorbent interactions are pretabulated with a grid

spacing of 0.2 Å and interpolated during the simulation for any position of the guest


species in the zeolite phase. [30,113] Four kinds of Monte Carlo moves, translational, ro-

tational, volume exchange, and particle transfer moves, are used to sample the phase

space. The coupled–decoupled configurational-bias Monte Carlo algorithm [59] is used to

enhance the acceptance rate for particle transfer moves. The probabilities for volume

and transfer moves are adjusted to have approximately one accepted move per Monte

Carlo cycle (MCC), where an MCC consists of a number of randomly selected moves

that is equal to the number of total molecules in the system (not counting the zeolite).

For all simulations, the probability to choose a molecule type for a transfer move is set

proportional to its overall mole fraction. The remaining moves are divided equally be-

tween translations and rotations. An equilibration period of at least 25000 MCCs is used

for each simulation trajectory, which is followed by a production period between 100000

to 150000 MCCs. For binary simulations, the Monte Carlo trajectory is divided into

five blocks, and uncertainties are estimated as the standard error of the mean for these

blocks. For four-component and five-component mixture simulations, eight independent

simulations were carried out with an equilibration for 15000 MCCs and a production

run of 25000 MCCs.

4.2.3 Data Analysis

An adsorbent can be characterized by several different attributes; here we define a perfor-

mance criteria that depends on two main properties: loading of desired sorbate molecule

at pre-specified adsorption conditions, QH2S, and equilibrium selectivity towards the

desired component, S, defined as:

S = (xH2S/xalkane)/(yH2S/yalkane) , (4.3)

where x and y are mole fractions in the adsorbed phase and the gas phase, respectively.

Mole fractions are computed for every configuration and are averaged over the entire

simulation trajectory. However, for zeolites where there are configurations with zero

adsorbed molecules, x cannot be defined for those configurations; in such cases, the

average loadings from the entire simulation trajectory are used to compute x.

As a first-order approximation, the cost for an adsorption step would be inversely

proportional to the loading. Contrary to this, if the target separation factor is 1000,


an adsorbent with a selectivity of 1000 would achieve this separation in a single step,

while adsorbents with a selectivity of 32 and 10 would require 2 and 3 steps, respectively.

Hence, for selectivity, (lnS)−1 would be a better representative of the cost of separation.

For each of the binary mixtures investigated in this work, we define the performance

criteria, PH2S, as the product ofQH2S and ln(S). This performance metric is quite general

and is not a function of any particular means of operating an adsorption process. Since

QH2S < 0.1 mmol g−1 is too low a loading of H2S for any practical application, zeolites

with such small loadings are assigned PH2S = 0, no matter how high their selectivity

towards H2S might be.

Using the adsorption isotherms that are fitted to the five different compositions,

we simulate a breakthrough column and calculate the number of adsorption stages to

achieve a target purity of 90 mole % H2S in the adsorbed phase for feeds with three

with increasingly high sourness quotient, yF = 0.10, 0.30, and 0.50. For example, if the

selectivity is high enough to meet the target adsorbed composition in a single stage, it will

be a 1-stage process. In case the target is not met, all of the adsorbed gas is desorbed and

is subjected to a second adsorption stage. One can continue this procedure to determine

the number of stages, n, that would be required to meet the target separation. For the

n-stage breakthrough column, it is assumed that the adsorption takes place at the inlet

composition at any stage and that all of the H2S from the incoming stream is adsorbed,

releasing no H2S at the outlet until breakthrough is attained. In addition to the number

of stages, we also estimate the total quantity of a particular zeolite, Mzeo, that would

be needed for the n-stage adsorption to remove 10 mmol of H2S. (This is not simply a

product of QH2S and n because loading can vary considerably with composition.)

For binary mixtures, the partial molar adsorption enthalpy for H2S is computed

as the average of difference between enthalpies of simulation frames having the same

number of adsorbed alkane (CH4 or C2H6) molecules.


Figure 1 shows binary H2S/CH4 and H2S/C2H6 adsorption data for all structures in-

vestigated in this work. We define the performance metric, PH2S, as the product of H2S

loading, QH2S, and the logarithm of selectivity toward H2S versus CH4 or C2H6, lnSM or


50 100 150 200 250 300 3500

10

20

30

50 100 150 200 250 300 350

50 100 150 200 250 300 350

PH

2S [

mm

ol g

-1]

or

Mzeo [

g]

0

10

20

50 100 150 200 250 300 350

50 100 150 200 250 300 350 4000

10

20

50 100 150 200 250 300 350 400

C

B

A

yF = 0.10

yF = 0.30

yF = 0.50

F

E

D

yF = 0.10

yF = 0.30

yF = 0.50

zeolite framework index

Figure 4.1: Binary H2S/CH4 (A, B, C) and H2S/C2H6 (D, E, F) adsorption at differentfeed concentrations of H2S: yF = 0.50 (A,D), 0.30 (B, E), and 0.10 (C, F) at T = 343 Kand p = 50 bar. Circles represent PH2S values, and the zeolite frameworks are orderedby PH2S at yF = 0.50 in a mixture with CH4. Cyan and yellow circles show data pointswith S ≥ 10 and S < 10, respectively. Black up and magenta down triangles show Mzeo

for structures that can achieve xT in one and two stages, respectively.

lnSE. PH2S is intrinsic to the properties of a sorbent and is independent of any specific

process design. We also define another performance metric which involves modeling of a

breakthrough column, and yF here refers to the inlet condition at the column. Estimates

are made for the number of stages and the total mass of a particular zeolite framework,

Mzeo, required to adsorb 10 mmol H2S at ≥ 90 mol% in the sorbent (xT ≥ 0.90).

The number of structures with SM ≥ 10 is significantly higher than those yielding

SE ≥ 10. The critical temperatures of CH4 and C2H6 are 0.51 and 0.82 times that of

H2S, respectively; thus, enthalpic contributions play a smaller role for SE than for SM.

Moreover, PH2S generally increases from yF = 0.10 to 0.50 because a higher fugacity of

H2S yields a higher QH2S, and this enhances sorbate–sorbate interactions contributing


S

1

10

100

1000

10000

∆H

ads [k

J m

ol -1

]

AH

T-1

AW

O-0

EP

I-1

AP

C-2

GIS

-5

GIS

-1

ME

L-1

JS

N-1

DF

T-0

PH

I-1

EP

I-0

SE

W-1

LT

L-1

ST

W-0

MF

I-1

DO

H-1

PA

U-1

SF

F-1

JS

N-0

UF

I-1

PH

I-2

GIS

-2

CA

S-0

CZ

P-0

AT

V-1

RS

N-0

WE

I-0

RW

R-1

RW

R-0

AB

W-0

MO

N-0

AP

C-1

LT

L-2

AC

O-0

AE

L-1

UE

I-0

ME

R-2

AF

Y-0

AP

D-0

AP

C-0

PH

I-0

VF

I-1

AE

T-1

MO

Z-1

PA

U-0

ME

P-1

MT

N-1

ITE

-1

IWV

-1

SB

N-0

SIV

-0

ITH

-1

JN

T-0

AT

V-0

JB

W-0

LO

V-0

ITW

-0

RR

O-0

VN

I-0

BIK

-0

ED

I-1

LT

J-0

-50

-40

-30

-20

-10

Figure 4.2: Selectivity (left axis) and ∆Hads (right axis) in top-performing zeolite struc-tures at yF = 0.50, T = 343 K, and p = 50 bar. Data for SM, SE, and ∆Hads are shownas cyan triangles, magenta squares, and green bars, respectively.

to increased selectivity. [126] Nonetheless, the correlation between PH2S at low and high

yF is quite good for both H2S/CH4 and H2S/C2H6 binary systems (see SI).

For a multi-stage adsorption process, the number of stages significantly impacts the

operating as well as capital expenditure. Shown also in Figure 1 are data for those zeolites

that can achieve xT in at most two adsorption stages. For the H2S/CH4 mixture at

yF = 0.50, 222 zeolites can accomplish this task in a single stage, and another 148 require

only two stages. For the H2S/C2H6 mixture, these numbers are 84 and 36, respectively.

The better performing zeolite structures for H2S/C2H6 separation range from ones that

perform very well to relatively poor for the H2S/CH4 mixture. Once again, the number

of zeolites that can reach xT drops significantly at lower feed compositions. This is due

to a decrease in S at lower yF, as well as an increase in the enrichment required to

achieve the same target from lower yF.

An adsorbent can have several attributes and depending on the application, one at-

tribute may be more important than the other. For instance, for gas storage applications,

the capacity of the adsorbent is a major factor determining the best adsorbent, but for

separation applications, selectivity towards the molecule of interest is more critical as

long as a reasonable capacity is reached. In Figure 2, we show the performance of the

top 62 adsorbents selected for SM ≥ 15 (44 sorbents) or SE ≥ 10 (29 sorbents). There


are 11 structures that satisfy both criteria: AHT-1, APC-1, AWO-0, ACO-0, APC-2,

GIS-1, APD-0, DFT-0, APC-0, SBN-0, JNT-0 (here, XYZ-0 represents a framework in

its idealized all-silica form and energy-optimized to avoid an unreasonably high-energy

structure, while XYZ-i (i = 1−6) correspond to the experimental structures [25] that are

taken as is but placing Si at all tetrahedral sites.) Also shown are data for the partial

molar adsorption enthalpies of H2S in the mixture with CH4, ∆Hads, that vary widely

between 23–46 kJ/mol. Although DOH-1 and MTN-1 yield only moderate SM, these

frameworks have very low |∆Hads|. In contrast, AHT-1 and APC-1 possess a very high

SM and SE but also show high |∆Hads|. This suggests that beyond high selectivity and

reasonable QH2S, sorbent selection can gain robustness by also including the regeneration

costs contingent on ∆Hads.

For the H2S/CH4 separation, SM values of top-performing frameworks fall below

60 with the exception of AHT-1 and APC-1 with SM > 300. These two structures are

found experimentally as hydrated aluminophosphates, and solvent removal for this study

resulted in very favorable pockets for H2S adsorption (as indicated by the high |∆Hads|).However, APC-0 and APC-2, which is a dehydrated experimental structure, also belong

to the set of top structures from this screening study. It should be noted that the loading

for APC-1, APC-2, and APC-0 are 4.0, 2.3, and 2.1 mmol g−1, respectively, suggesting

partial framework shrinkage on dehydration. For the top-performing experimentally

hydrated structures (AHT-1, APC-1, LTL-2, EPI-1, GIS-5, GIS-1, PHI-1, VFI-1, LTL-1,

PAU-1, PHI-2, GIS-2, EDI-1), our inference is that these will indeed be good structures

for sour gas sweetening if their energy-minimized analogs also offer similar PH2S and

Mzeo, i.e., it is the physical framework that enhances separation, rather than favorable

pockets formed by water removal.

A large fraction of the high-performing structures contain periodic building units that

can be constructed from either a zigzag chain, a saw chain, or a crankshaft chain. [25] For

H2S/CH4 separation, about 75% of the top selectivity structures contain a crankshaft

chain and, conversely, about 60% of all frameworks having a crankshaft chain yield

SM ≥ 15. These selective structures allow for QH2S between 1.5–6.5 mmol g−1. Most

structures with SM < 15 but SE ≥ 40 contain either a zigzag or a saw channel, but exhibit

a relatively lower QH2S of 0.5–2.5 mmol g−1. Most of the top-performing structures

(APC, AWO, ACO, GIS, APD, DFT, SBN, JNT) contain eight-membered rings as the


yi

0

0.25

0.5

0.75

1H

2S CO

2CH

4C

2H

6N

2x

i

0

0.25

0.5

0.75

AH

T-1

AP

C-1

AW

O-0

AP

C-2

AC

O-0

AE

L-1

GIS

-1

DFT-0

AP

D-0

AFY

-0

AP

C-0

JN

T-0

SB

N-0

ATV

-0

ATV

-1

BIK

-0

Figure 4.3: Five-component adsorption at T = 343 K and p = 50 bar using aH2S:CO2:CH4:C2H6:N2 feed composition with molar ratio of 25:10:50:10:5. Equilib-rium mole fractions in the gas phase (top) and in the adsorbed phase (bottom) for 16high-performing zeolite structures.

limiting pore diameter. While treating the zeolite as rigid is a good assumption in most

cases, framework flexibility is likely to influence the dynamic accessibility for molecules

with dimensions comparable to the limiting pore diameter. [130] A concerted resonse

involving the local zeolite structure and the sorbate conformation may play a role in

adsorption kinetics and accessibility of selective adsorption sites.

From the set of 62 top structures shown in Figure 2, we select 16 structures to probe

their performance for a five-component mixture involving H2S, CO2, CH4, C2H6, and

N2 in a 25:10:50:10:5 mole ratio (see Figure 3). The equilibrium composition attained in

such a (virtual) system depends on the initial feed composition and the mole (or weight)

ratio of zeolite sorbent contacted with the gas mixture (see SI for details). A larger

amount of sorbent would further reduce the mole fraction of H2S in the gas phase at

the expense of decreased hydrocarbon recovery. Additionally, we also investigate a four-

component mixture (H2S:CO2:CH4:C2H6 with a molar ratio of 16:10:70:4, see Figure S3)


representative of the Lacq gas, [131] that has a H2S:CH4 ratio over twice that of the five-

component mixture. We find that SM and SE values are very similar for the binary and

four- and five-component mixtures (see Figure S4); this indicates that binary mixtures

can be used for screening purposes. Ranking the performance of zeolite structures by

the ratio of the percentage of H2S removed over the percentage of carbon lost due to

adsorption yields a very high correlation for these complex four- and five-component

mixtures (R2 = 0.98, see Figure S5). The AHT-1 and APC-1 structures with their

very high SM and high SE values adsorb the least amount of hydrocarbons. However,

these structures differ in H2S/CO2 selectivity resulting in APC-1 removing more H2S

but less CO2. This is further accentuated by comparing AWO-0 and BIK-0; the former

is very selective for H2S over CO2 and yields the highest xH2S, whereas the latter is very

selective for CO2 and adsorbs the least combined amount of these acid gases so that it

does not significantly lower the H2S concentration in the gas mixture.

Of all the top-performing structures presented in Figure 2, CAS, DOH, ITE, ITH,

ITW, MEL, MEP, MFI, MTN, RRO, RWR, and SFF frameworks have been synthesized

in all-silica form, IWV with a Si/Al ratio of 29, SEW with a Si/B ratio of 13, and

ABW, BIK, EDI, EPI, GIS, JBW, LTJ, LTL, MER, MON, MOZ, PAU, PHI, and UFI

with a low to moderate Si/Al ratio [25] and their high-silica defect-free analogs can be

interesting synthesis targets for the sour gas sweetening application. Selecting from the

already-synthesized zeolites, MEL and RWR are the best candidates for gas feeds lean

and rich, respectively, in ethane and other light alkanes.

4.4 Conclusion

In conclusion, we identified zeolitic sorbents that can enable selective removal of H2S

from CH4 and C2H6. A good correlation is found for the performance of these zeolites

when applied to four- and five-component mixtures representing highly sour and ultra-

sour gas reservoirs. However, the choice of optimal sorbent for sour gas sweetening

will depend on the relative importance of CO2 removal and the desire to reduce losses of

C2H6 and other light alkanes. This computational study shows promise for (ultra) highly

sour natural gas sweeting with hydrophobic zeolites and opens avenues for experimental

studies and process optimization.

Chapter 5

Transferable Potentials for Phase

Equilibria. Improved United-Atom

Description of Ethane and Ethylene

From M. S. Shah, M. Tsapatsis, and J. I. Siepmann, AIChE J. 2017, 63, 5098–5110.

Copyright c© 2017 by American Institute of Chemical Engineers. Reprinted by per-

mission of John Wiley & Sons, Inc. https://onlinelibrary.wiley.com/doi/abs/10.

1002/aic.15816

5.1 Introduction

Ethylene is the most important chemical building block with a global capacity of ap-

proximately 150 million metric tons per year (mmtpy) in 2015. [4] To cater to the world

ethylene demand growing at 5 mmtpy, [132] numbers and sizes of ethylene crackers are on

the rise. Ethylene synthesis involves a high-temperature steam cracking of diverse feed-

stocks such as ethane, propane, butane, and naphtha. The resulting cracking mixture

is subjected to a train of distillation columns to obtain high purity hydrocarbons. The

ethane/ethylene splitter (C2 splitter) operates at cryogenic temperatures (−30◦ C) and

moderately high pressures (2 MPa). [133] High-purity ethylene forms the distillate and

ethane obtained at the bottom of the column is recycled to the cracker feed. Since the

74

https://onlinelibrary.wiley.com/doi/abs/10.1002/aic.15816

https://onlinelibrary.wiley.com/doi/abs/10.1002/aic.15816

Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 75

ethane/ethylene relative volatility ranges between only 1.5 to 3.0, alternative separation

techniques, with higher separation factors and at higher temperatures, can contribute

to energy and cost savings.

Development of molecular force fields for alkanes [34,35,134–141] and alkenes [137,138,142–150]

has continued to be the research focus of several groups since the late 1990s. Most

of these force fields are based on vapor–liquid equilibria (VLE) as the primary prop-

erty in the training set. [34,35,134–139,142–147] Several groups presented force fields tuned

to reproduce adsorption in zeolites. [140,141,148–150] While almost all force fields use 12–6

Lennard-Jones potential to describe the van der Waals interactions, Errington and Pana-

giotopoulos used Buckingham exponential–6 potential for alkanes. [135] These authors also

introduced C–C bond lengths that are higher than the experimental value of 154 pm.

More recently, Potoff and Bernard-Brunel utilized Mie potentials that include the re-

pulsive power as an adjustable parameter. [139] In addition to the liquid densities and

critical temperatures for earlier united-atom models for alkanes, [34,35] these additional

parameters in the force field fitting allow to accurately reproduce the vapor pressures.

Similar efforts to account for the position of C–H valence electrons being closer to the

C–H bond centers, than at the C position, were undertaken by Ungerer et al. [136] and

Vrabec et al. [137] In addition to the anisotropic nature of ethane and ethylene, Vrabec

et al. also considered a point quadrupole to account for the electrostatic interactions in

case of various quadrupolar molecules, including ethane and ethylene. [137] In another at-

tempt to mimic the quadrupolar interactions of ethylene, Weitz and Potoff investigated a

three-site point charge model. [146] The results showed a slight improvement in pure ethy-

lene and xenon/ethylene binary VLE, but failed to predict the experimentally-observed

maximum pressure azeotrope for CO2 /ethylene mixtures.

In this work, we develop an improved version of the transferable potentials for phase

equilibria – united atom force field (hereafter referred as TraPPE–UA), namely TraPPE–

UA2, for ethane and ethylene. Liquid densities, critical temperature, and vapor pressures

of pure-component ethane are included in realizing a two-site ethane model. In addition

to the pure component properties, binary VLE with ethane, CO2, and H2O are also

included in training a four-site ethylene model.



The ethane and ethylene models investigated in this work, previous TraPPE–UA models

for ethane and ethylene, [34,143] TraPPE all-atom model for CO2, [55] and also the TIP4P

and TIP4P/2005 water models [151,152] are all non-polarizable and have a rigid geometry.

Non-bonded interactions are modeled using a pairwise-additive potential consisting of

Lennard-Jones (LJ) 12–6 and Coulomb terms:

U(rij) = 4εij

[(σijrij

)12

−(σijrij

)6]

+qiqj

4πε0rij, (5.1)

where rij , εij , σij , qi, and qj are the site-site separation, LJ well depth, LJ diameter, and

partial charges for beads i and j, respectively. Different combining rules for the unlike

Lennard-Jones parameters, such as Lorentz-Berthelot: [56]

σij =σii + σjj

2and εij =

√εiiεjj , (5.2)

Kong: [153]

εijσ6ij = (εiiσ

6iiεjjσ

6jj)

1/2 and εijσ12ij =

[(εiiσ

12ii )1/13 + (εjjσ

12jj )1/13

2

]13

, (5.3)

and Waldman–Hagler: [154]

σij =

[σ6ii + σ6

jj

2

]1/6

and εij =√εiiεjj

σ3iiσ

3jj

σ6ii+σ

6jj

2

, (5.4)

are assessed along the course of this work.

Ethane is a two-site model with three parameters, namely, the LJ diameter and well

depth (σ, ε) and the distance between the LJ sites (l). The pure-component VLE of

ethane, including the liquid densities, critical temperature, and vapor pressures over the

entire temperature range, is used to parametrize the ethane model. The parameters

selected for the TraPPE–UA2 model are reported in Table 5.1.

Ethylene is a four-site molecule with two LJ sites separated by a distance l along

the C–C bond length (see Figure 5.1). Positive partial charges (qC) are located on these


Table 5.1: Force field parameters: geometry, LJ parameters, and partial charges.molecule model l lEE εCC/kB σCC qC

[pm] [pm] [K] [pm] [|e|]C2H6 TraPPE–UA [34] 154 N/A 98 375 N/AC2H6 TraPPE–UA2 230 N/A 134.5 352.0 N/AC2H4 TraPPE–UA [143] 133 N/A 85 367.5 N/AC2H4 TraPPE–UA2 170 130 99.8 357.5 +0.32

lOH lOM εOO/kB σOO qM qHH2O TIP4P [151] 95.72 15 78.02 315.358 −1.04 +0.52H2O TIP4P/2005 [152] 95.72 15.46 93.2 315.89 −1.1128 +0.5564

lCO εCC/kB σCC εOO/kB σOO qCCO2 TraPPE [55] 116 27 280 79 305 +0.70

Figure 5.1: Schematic drawings of ethane and ethylene models of the TraPPE–UA [34,143]

and TraPPE–UA2 force fields.

sites and negative partial charges of magnitude qC are located on the perpendicular

bisector of the C–C bond with a separation of lEE. These negative partial charges

mimic the π-bonded electrons of ethylene. The five parameters can be grouped into two

categories: (i) the charge distribution (q and lEE) and (ii) the molecular shape as defined

by the distance between the LJ interaction sites (l) and the LJ parameters (σ, ε). Only

three parameters maybe uniquely defined in fitting to the property of highest interest,

namely, the pure-component VLE. We choose l and lEE, one from each category, to be

the independent parameters, and for each set of these independent parameters, we can


arrive at a set of qC, σ, and ε that describes the pure-component VLE of ethylene, almost

equally accurately. The binary phase equilibria of ethane/ethylene is used to constrain

the value of l and the LJ parameters. The parameter lEE and the corresponding charges

are further constrained by reproducing the interactions with water. The parameters

selected for the TraPPE–UA2 force field are reported in Table 5.1.

CO2 is modeled as a rigid, three-site molecule with LJ interaction sites and partial

charges on each of the three atoms with parameters taken from the existing TraPPE

force field [55]. Two different water models, TIP4P and TIP4P/2005, are assessed for its

binary phase equilibria with ethane or ethylene. Each of the water models uses a four-

site representation with a single LJ interaction site on oxygen, partial positive charges

on the hydrogens, and a compensating negative charge on the M-site, that is displaced

by a distance lO−M in the plane of the molecule towards the hydrogen atoms. Force field

parameters for both CO2 and H2O are listed in Table 5.1.

Gibbs Ensemble Monte Carlo (GEMC) simulations [31,40] in the canonical (NV T )

ensemble are used to simulate pure and binary (C2H6/C2H4, C2H6/H2O, C2H4/CO2,

and C2H4/H2O) VLE. For computing the Txy diagram for ethane/ethylene at a fixed

pressure, NV T -Gibbs ensemble simulations are setup at different compositions and tem-

peratures, and the pressures are computed. Using the current p of the system and the

knowledge of the pure-component Antoine-equation for ethane, a target T is computed

to achieve the target p for the Txy diagram, and the simulation is then run at this new

T . This procedure is repeated until convergence of less than 1% variation in simulated

p from the target p is achieved. This iterative procedure was found to be more efficient

than NpT -GEMC simulations, that suffer from large fluctuations in phase ratio due to

the small separation factors.

System sizes (N) of 1500 and 1000 total molecules are used to compute the unary

VLE for ethane (covering temperatures from 178 to 295 K) and ethylene (covering tem-

peratures from 170 to 270 K), respectively; for a few high-temperature state points,

N = 12 000 and 8000 are also considered for ethane and ethylene, respectively. A total

of 1000 molecules, with varying composition, is used for the C2H6/C2H4 and C2H4/CO2

binary systems. For the binary simulations with H2O, 1000 molecules of H2O and 500

molecules of either C2H6 or C2H4 are used.

LJ interactions are truncated at 1.4 nm and analytical tail corrections are applied.


The Ewald summation method [33] with a screening parameter of κ = 3.2/rcut and

Kmax = κLbox + 1 for the upper bound of the reciprocal space summation is used

for the calculation of the Coulomb energy. The total system volume is adjusted for each

state point to yield a vapor phase containing about 10–20% of the molecules. [58] Since

this can lead to rather large volumes (and, correspondingly, linear dimensions) of the

vapor-phase box, rcut for the vapor phase is set to approximately 40% of the box length

to reduce the cost of the Ewald sum calculations. Four kinds of Monte Carlo moves, in-

cluding translational, rotational, volume exchange, and particle transfer moves, are used

to sample the phase space. The coupled-decoupled configurational-bias Monte Carlo

algorithm [59] is used to enhance the acceptance rate for particle transfer moves. The

probabilities for volume and transfer moves are set to yield approximately one accepted

move per Monte Carlo cycle (MCC), [58] where a MCC consists of N randomly selected

moves. The remaining moves are divided equally between translations and rotations.

An equilibration period of 50 000 to 100 000 MCCs is used for all simulations.

1 000 000 and 400 000 MCCs are used for the production run of unary ethane and ethy-

lene systems, respectively. 50 000− 200 000 production cycles are used for C2H6/C2H4

and CO2/C2H4 binary simulations. 100 000 and 200 000 production cycles are used for

H2O/C2H4 and H2O/C2H6 binary simulations, respectively. For all systems investigated

in this work, eight independent simulations are carried out at each state point and the

statistical uncertainties reported in the following sections are the standard errors of the

mean calculated from these independent simulations.


It is important to note that this work replaces a search in the full three- or five-

dimensional space for ethane or ethylene, respectively, with a process where only the

Lennard-Jones parameters (and partial charges in case of ethylene) are optimized for

a given l. This work considers a step-size of 10 pm for l, and the LJ parameters and

charges are optimized using steps of 0.1 K, 0.1 pm, and 0.01 e for ε/kB, σ, and qC,

respectively. The steps for the LJ parameters and partial charges reflect the precision

of the simulations. This work does not use a predetermined objective function because

the sensitivity of the model to different properties is not known a priori, and in some


0 100 200 300 400 500 600

ρ [kg/m3]

160

200

240

280

320

T [

K]

Experiment [NIST]

TraPPE--UA

l = 220 pm

l = 230 pm

l = 240 pm

l = 250 pm

Figure 5.2: Vapor–liquid co-existence curves for ethane. Experimental data, shown as aline and black filled symbol for the critical point, are taken from NIST. [155] Statisticaluncertainties for the simulation data are smaller than the symbol size.

cases, decisions need to be made not following strictly numerical guidelines. Following

the stepwise details of the model development discussed below will help understand this

point better.

5.3.1 Unary ethane VLE

Vapor–liquid coexistence curves and Clausius-Clapeyron plots for various ethane mod-

els are shown in Figures 5.2 and 5.3 (numerical data are reported in Table S1 in the

Supporting Information1), respectively. Figure 5.4 shows the percentage deviation in

vapor pressures, vapor densities, and liquid densities over a wide temperature range for

vapor–liquid co-existence. For the calculation of the critical properties, saturated liquid

and vapor densities at T ≥ 280 K (i.e, T ≥ 0.9Tc) are fitted to the scaling law for the1https://onlinelibrary.wiley.com/action/downloadSupplement?doi=10.1002%2Faic.15816&

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3 3.5 4 4.5 5 5.5 61000/(T [K])

4

5

6

7

8

9

ln(p

[k

Pa]

)

Experiment [NIST]

TraPPE--UA

l = 220 pm

l = 230 pm

l = 240 pm

l = 250 pm

5.617 5.618 5.6191000/(T [K])

4.2

4.25

4.3

ln(p

[k

Pa]

)

Figure 5.3: Logarithm of saturated vapor pressures versus inverse temperature forethane. Experimental data, shown as black line, are taken from NIST. [155] The insetzooms in to the lowest temperature data.

critical temperature: [71]

ρliq(T )− ρvap(T ) = A(T − Tc)β (5.5)

and the law of rectilinear diameters: [72]

ρliq(T ) + ρvap(T )

2= ρc +B(T − Tc) (5.6)

where β = 0.326 is the universal critical exponent for three-dimensional systems. [159]

The critical pressure is determined by extrapolating the Antoine equation to to the

computed critical temperature. The normal boiling point is obtained by interpolation

of the Clausius-Clapeyron equation between the two data points closest to Tb. The

normal boiling points, critical properties, and acentric factor for the ethane models are

summarized in Table 5.2.

Figure 5.4 shows that the estimation of high-temperature liquid and vapor densities,


180 200 220 240 260 280 300T [K]

0

2

4

6

10

0∆

ρli

q/ρ

liq

-8

-4

0

4

10

0∆

ρv

ap/ρ

vap

l = 220 pm

l = 230 pm

l = 240 pm

l = 250 pm

-4

-2

0

2

4

10

0∆

p/p

Figure 5.4: Percentage errors with respect to the experimental measurements [155] invapor pressure (top), vapor density (middle), and liquid density (bottom) versus tem-perature for different ethane models. Statistical uncertainties for the simulation dataare smaller than the symbol size.

and therefore even the critical properties, may be improved to some extent by choosing

a higher value of l. Table 5.2 further demonstrates that with an increase in the value of

l beyond 230 pm, for equally accurate critical pressures, there is slight improvement in

the critical temperatures, but at the cost of over-prediction in the normal boiling points.

However, it should be noted that since the C–C and C–H bond lengths in ethane are

154 and 110 pm, respectively, with the C–C–H bond angle being 110.7◦, the physical

distance between the LJ sites in the simplest case of a two-site model, obtained by the

projection of hydrogen atoms along the C–C bond, should be < 232 pm. This argument

is somewhat qualitative since there are three hydrogen atoms that need to be projected


Table 5.2: Normal boiling point, critical properties, and acentric factors for ethane.model Tb Tc ρc pc ω

[K] [K] [kg/m3] [MPa]TraPPE–UA (N = 400) [34] 1771 3042 2063 5.14TraPPE–UA (N = 1500) 176.21 302.84 2181 5.21 0.022l = 220 pm (σ = 355 pm, ε/kB = 130 K) 184.084 308.93 2141 5.11 0.072l = 230 pm (σ = 352.0 pm, ε/kB = 134.5 K) 184.502 308.62 2141 5.11 0.082l = 240 pm (σ = 349.3 pm, ε/kB = 138.8 K) 184.842 308.31 214.13 5.095 0.091l = 250 pm (σ = 347 pm, ε/kB = 143 K) 185.313 308.13 2121 5.11 0.102Experiment 184.6 [156] 305.33 [155] 20712 [155] 4.91 [155] 0.102 [155]

184.5 [157] 305.324 [158] 2063 [158] 4.871 [158]

Subscripts denote the standard error of the mean for the last digit(s).Superscripts denote the sources for the experimental data and previous simulations.

and also the centers of polarizability are somewhere along the C–H bond and not at the

H atoms. Nonetheless, it suggests that two-site Lennard-Jones models with even higher

l, to slightly improve the prediction of critical properties (at the expense of inaccurate

temperature dependence of the vapor pressure) are likely to be unphysical.

Pitzer’s acentric factor, [160] ω, is a measure of the relative steepness of the vapor

pressure curve and is defined as:

ω = − log10[p(T )/pc]− 1 at T = 0.7Tc. (5.7)

A value of ω = 0 is found for simple spherical particles, such as noble gases and methane.

It can be seen that while all the ethane models assessed here with l between 220–250 pm

are in agreement with the experimental value of ω, within statistical and experimental

uncertainties, TraPPE–UA, with l = 154 pm, highly under-estimates the acentric factor.

Thus, the more elongated shape of the TraPPE–UA2 model allows one to capture bet-

ter the temperature dependencies of the enthalpy and entropy changes associated with

vapor–liquid transfer, whereas the TraPPE–UA model yields an ω value that is closer

to that found for spherical particles.

It should be noted here that although our earlier simulations for TraPPE–UA [34]

used a smaller system size and included lower temperature data for the determination of

the critical point (T ≥ 0.9Tc in this work versus T ≥ 0.7Tc in the earlier work), and even

though the applicability of the Ising scaling law far away from Tc is questionable, the

newly computed critical temperature is within the statistical uncertainty of the previous

data, however, the critical density was underestimated in the earlier simulations. Earlier

estimates used a critical exponent of 0.32, as opposed to 0.326 in this work.


Table 5.2 also lists the optimized LJ parameters for each bond length. For the model

with l = 230 pm, parameters can be found that satisfy the target accuracy for the unary

VLE of C2H6. The uncertainty in experimental normal boiling points from most recent

measurements [156,157] is less than 0.1% and this model exactly reproduces the boiling

point, and the saturated vapor pressures fall within 1.2% of the experimental values over

the entire temperature range from below the normal boiling point to the near-critical

region. The saturated liquid and vapor densities are within 1% of the experimental

value for T < 0.8Tc; however, the deviations start to increase rapidly as the critical

temperature is approached. It is somewhat surprising that the models yield very accurate

vapor pressures at T > 280 K, but quite large differences in the vapor density. That is,

the compressibility factors obtained from models and experiment diverge as the critical

point is approached. High-temperature data (T = 280−295 K) for an eight times larger

system size for ethane (N = 12 000), with two different values of cutoffs (1.4 and 2.8 nm),

run for at least 150 000 and 50 000 MCCs, respectively, using the k-d tree data structure

implementation, [161] are provided in the Supporting Information (see Table S3). With

the exception of the vapor pressure and density at T = 295 K, the system size effect is

negligible.

In the experimental measurement of the two-phase envelope, pressure and density

are measured along the isotherms in the vapor–liquid coexistence region and also in the

adjacent single-phase vapor and liquid regions. [162] The saturated liquid-density curve

is located from the sharp intersection of the extrapolated liquidus isotherms and the

corresponding two-phase isobars on a pressure–density grid. However, the authors of

the experimental paper describe that a similar strategy to obtain the saturated vapor-

density curve was rather difficult due to the precondensation of gaseous ethane that

resulted in a rounded (unsharp) intersection of the two lines even at temperatures as

low as 0.9Tc. However, the extent of systematic errors in the experimental vapor densities

are not clear and this issue will warrant further consideration in future work. In our

parametrization, we decided to place more weight on the experimental vapor pressure

data.

The critical temperature for this model is over-estimated by 1%. It should be noted

that the current parametrization places emphasis on accurate vapor pressures and to


Table 5.3: Optimized parameters for different ethylene models.

l lEE qC εCC/kB σCC

[pm] [pm] [|e|] [K] [pm]

130 130 0.53 81.4 374.2150 130 0.41 90.6 365.4170 0 0.47 99.8 357.5

80 0.41 –"– –"–130 0.32 –"– –"–180 0.23 –"– –"–

200 130 0.17 114.4 346.1

some extent tolerates a larger error for the critical temperature compared to the TraPPE–

UA parametrization. Even a small error in the critical temperature leads to a sharp rise

in the errors for the liquid and vapor densities as one approaches the critical temperature

due to the flatness of the vapor–liquid coexistence curve in this region. Although the

critical density is over-estimated by about 3% from the mean experimental value, the

uncertainty in the experimental value can be between 1–6%. [155,158] The critical pressure

is about 5% above the experimental value, but the simulated and experimental uncer-

tainties are about 2%. [155,158] Uncertainty estimation for the force field parameters of

ethane revealed that the parameters are extremely coupled. Equally accurate models

could likely be obtained for l between 228–232 pm, provided the ε and σ parameters are

optimized for each l. It is worth noting here that as the separation factors for mixtures

approach unity, the sensitivity of the equipment sizing and cost to the phase equilib-

ria increases exponentially. The TraPPE–UA2 models place a premium on getting the

separation factors extremely accurately, even though this would mean a slightly higher

error in the critical properties, unlike the TraPPE–UA models.

5.3.2 Unary ethylene VLE

Table 5.3 lists different sets of parameters optimized for pure-component VLE of ethy-

lene. As mentioned earlier, l and lEE are chosen independently, with step sizes of 20 and

50 pm, respectively, and the remaining three parameters are optimized to accurately

reproduce the vapor pressures and the liquid and vapor densities upto about 90% of

critical temperature. Note that lEE = 0 pm corresponds to a three-site model, where


Table 5.4: Normal boiling point, critical properties, and acentric factors for ethylene.model Tb Tc ρc pc ω

[K] [K] [kg/m3] [MPa]

TraPPE–UA (N = 400) [143] 1641 2831 2152TraPPE–UA (N = 1500) 162.91 281.13 2261 5.32 0.014TraPPE–UA2 169.543 286.34 2231 5.32 0.064Experiment 169.3 [156] 282.55 [155] 2142 [163] 5.065 [155] 0.091 [155]

169.35 [164] 282.342 [163] 5.0414 [163]

Subscripts denote the standard error of the mean for the last digit(s).Superscripts denote the sources for the experimental data and previous simulations.

the charge on the central site is −2qC. Just like for ethane, an increase in l for ethylene

is accompanied with a decrease in σCC (to compensate for the size) and an increase in

εCC. The choice of l uniquely defines the LJ parameters to achieve accurate temperature

dependence of the vapor pressure. lEE can be set independently, and the corresponding

charge value can be adjusted to yield equally accurate unary VLE. In some other sys-

tems, we have observed that the convergence of Ewald summation becomes increasingly

expensive when the smallest distance between any two charges in the system decreases.

In the case of commonly used TIP4P-type water models, the distance between the neg-

ative charge on the M site and the positive charge on the H atoms is about 87 pm.

Therefore we chose minimum lEE value for the four-site ethylene models to be 80 pm

and then explored two other models in steps of 50 pm (130 and 180 pm). There is some

limit to how much one can increase lEE, since even higher values result in a strong un-

physical binding of the unprotected electron sites to the unprotected positive H atoms

in case of water.

Figure 5.5 shows the percentage errors in liquid and vapor densities and saturated

vapor pressures as a function of temperature. It can be seen that the different ethy-

lene models are almost equally accurate. Even higher similarity in the models may be

achieved by adding additional precision to the parameters, specially the charge param-

eter, that has only two significant digits. However, additional criteria are required to

decide between these models. Binary phase equilibria with ethane and with water (dis-

cussed below) help to further constrain the model and the model with l = 170 pm and

lEE = 130 pm is chosen here.

Figures 5.6 and 5.7 show the vapor–liquid coexistence curves and Clausius-Clapeyron


165 180 195 210 225 240 255 270T [K]

0

2

4

6

10

0∆

ρli

q/ρ

liq

-12

-8

-4

0

10

0∆

ρv

ap/ρ

vap

l = 130 pm lEE

= 130 pm

l = 150 pm lEE

= 130 pm

l = 170 pm lEE

= 0 pm

l = 170 pm lEE

= 80 pm

l = 170 pm lEE

= 130 pm

l = 170 pm lEE

= 180 pm

l = 200 pm lEE

= 130 pm

-2

-1

0

1

10

0∆

p/p

Figure 5.5: Percentage errors with respect to the experimental measurements [155] invapor pressure (top), vapor density (middle), and liquid density (bottom) versus tem-perature for different ethylene models. If not shown, error bars are smaller than symbolsize.

plots for ethylene, respectively, and Table 5.4 compares the normal boiling points, the

critical properties and the acentric factors. The uncertainty in experimental normal

boiling points from most recent measurements [156,164] is less than 0.03% and this model

reproduces this value within 0.1%, and the saturated vapor pressures fall within 1.5% of

the experimental values over the entire temperature range from the normal boiling point

to the near-critical region. The saturated liquid and vapor densities are within 1.5% of

the experimental value for T ≤ 0.75Tc; however, the deviations start to increase rapidly

as the critical temperature is approached. The critical temperature for this model is

over-estimated by 1.5% and although the critical density is over-estimated by about 4%


0 100 200 300 400 500 600

ρ [kg/m3]

160

180

200

220

240

260

280

T [

K]

Experiment [NIST]

TraPPE--UA

TraPPE--UA2

Figure 5.6: Vapor–liquid co-existence curves for ethylene. Experimental data, shown asa line and black filled symbol for the critical point, are taken from NIST. [155]

from the mean experimental value, the uncertainty in the experimental value is 1%. [163]

The critical pressure is about 5% above the experimental value, but the simulated and

experimental uncertainties are about 1%. [155,163]. The acentric factor for the TraPPE–

UA2 model, compared to the TraPPE–UA model, is in much better agreement with the

experimental value, suggesting that the former better captures the changes in transfer

enthalpy and entropy with temperature for the ethylene molecule. Similar to the ethane

model, the uncertainty estimation for the ethylene parameters revealed that the param-

eters are extremely coupled, and independent uncertainties cannot be assigned to each

parameter.

5.3.3 Binary ethane/ethylene VLE

Ethane and ethylene constitute a large fraction of the natural gas liquids and form major-

ity of products of an ethylene cracker with ethane as the feedstock. These molecules are

most commonly separated by cryogenic distillation and thus their mixture vapor–liquid


3.5 4 4.5 5 5.5 61000/(T [K])

5

6

7

8

9

ln(p

[k

Pa]

)

Experiment [NIST]

TraPPE--UA

TraPPE--UA2

Figure 5.7: Logarithm of saturated vapor pressures versus inverse temperature for ethy-lene. Experimental data, shown as black line, are taken from NIST. [155]

phase equilibria is of significant interest to many gas and petrochemical industries. Al-

ready in 1976, Fredenslund et al. reported on measurements of the binary VLE at 263.15

and 293.15 K. [165] This was followed in 1982 by the work of Barclay et al. [166] covering

a wider range of 198.15 K ≤ T ≤ 278.15 K. This was followed by the work of Calado et

al. at 161.39 K. [167] Considering the practical importance of this system and for improv-

ing the transferability of the ethylene force field, binary VLE for the ethane/ethylene

mixture are considered as an additional criterion in the force field development.

The sensitivity of relative volatility,

α =y/(1− y)

x/(1− x), (5.8)

where x and y are the mole fractions of the more volatile component in the liquid and

vapor phases, respectively, to the change in composition increases at lower tempera-

tures. Hence, we chose the lowest temperature at which experimental data are available


(161.39 K) for assessing the different ethylene models. Figure 5.9 shows the pressure–

composition diagram and separation factors for the different ethylene models alongwith

the TraPPE–UA2 ethane model. Note that the relative volatility shown for TraPPE–

UA is computed using the UA version of the TraPPE force field for both ethane and

ethylene. The pxy data for the ethylene models with lEE = 130 pm show an increased

solubility of ethylene in ethane with an increase in l from 130 pm to 200 pm. This en-

hancement in the solubility comes from the shift in the interaction strength of ethylene

from first-order electrostatic to dispersive LJ, since increasing l leads to an increase of

the value for the LJ well-depth and a decrease of magnitude of the partial charges (see

Table 5.3). When a mixture obeys Raoult’s law, the relative volatility is simply equal to

the ratio of the pure component vapor pressures of the two species at the temperature

of interest and there is no dependence of this quantity on the composition. Clearly,

the experimental relative volatility decreases by about 50% in going from an ethane-rich

liquid to an ethylene-rich liquid. The TraPPE–UA model predicts Raoult’s law behavior

with a constant relative volatility (α ≈ 2.2), suggesting that it cannot capture the subtle

differences in the interactions of ethane and ethylene resulting from preferential solva-

tion. The ethylene molecules benefit from enhanced first-order electrostatic interactions

with other ethylene molecules in an ethylene-rich liquid for the non-polarizable mod-

els (induced polarization would become a factor for polarizable models, and require a

slightly smaller static quadrupole moment), compared to fewer such special interactions

when the liquid is ethane-rich. This explains the lower relative volatility of ethylene at

higher liquid-phase mole fraction of ethylene. l = 170 pm results in a subtle balance

of first-order electrostatics and dispersive interactions that allows accurate prediction of

the compositional dependence of the relative volatility.

Figure 5.8 shows the binary phase equilibria at a higher temperature of 263.15 K.

While the propagated uncertainty in relative volatility from experiments is quite high,

TraPPE–UA2 performs better than TraPPE–UA. The pxy diagram for TraPPE–UA is

shifted above the experimental data of Fredenslund et al. [165] by about 20% for ethane-

rich mixtures and by about 10% for ethylene-rich mixtures. These results indicate the

superior performance of the new force fields for mixture predictions over a wide temper-

ature range.


0 0.2 0.4 0.6 0.8 1x

C2H

4

, yC

2H

4

2000

2500

3000

3500

p [

kP

a]

0 0.2 0.4 0.6 0.8 1

xC

2H

4

1.2

1.4

1.6

1.8

α

Fredenslund et al.

TraPPE--UA

TraPPE--UA2

Figure 5.8: Binary ethane–ethylene phase behavior: pressure–composition diagram (bot-tom) and relative volatility–composition dependence (top) at T = 263.15 K for TraPPE–UA and the TraPPE–UA2 models for ethane and ethylene. If not shown, statistical un-certainties for the simulation data are smaller than the symbol size. The experimentaldata are taken from Fredenslund et al. [165]

It can also be seen that the binary phase behavior of ethylene with ethane is indepen-

dent of lEE. This is because lEE only influences the electrostatics of ethylene and there

are no partial charges in the ethane model (see Figure 5.9 for close agreement of models

with lEE = 130 and 180 pm). Therefore, the binary phase behavior with a more polar

molecule may help in uniquely defining the value of lEE and, hence, the corresponding

qC. But before moving on to the other binary systems, it is worthwhile to discuss here

the effect of differences in relative volatility predicted by the two different versions of

the TraPPE force field on the design of a distillation column to separate a mixture of

ethane and ethylene.


0 0.2 0.4 0.6 0.8 1x

C2H

4

, yC

2H

4

20

30

40

50

60

p [

kP

a]

0 0.2 0.4 0.6 0.8 1

xC

2H

4

1

2

3

4

α

Calado et al.

TraPPE--UA

l = 130 pm; lEE

= 130 pm

l = 150 pm; lEE

= 130 pm

l = 170 pm; lEE

= 130 pm

l = 170 pm; lEE

= 180 pm

l = 200 pm; lEE

= 130 pm

Figure 5.9: Binary ethane–ethylene phase behavior: pressure–composition diagram (bot-tom) and relative volatility–composition dependence (top) at T = 161.39 K for TraPPE–UA2 ethane model and ethylene models with varying l and lEE. Since the deviationsin vapor pressures of TraPPE–UA mixtures are quite high, only the relative volatilitydata are shown (numerical pxy data are included in the supporting information). Theexperimental data are taken from Calado et al. [167]

The saturation vapor pressures predicted by TraPPE–UA and TraPPE–UA2 models

are quite different (see Figures 5.3 and 5.7). So to compare distillation performance

at similar overhead and bottoms temperatures, the binary VLE for this mixture were

computed at two different overall pressures, i.e., 2 MPa for TraPPE–UA2 and 2.4 MPa for

TraPPE–UA (see simulation details for a description of how isobaric mixture properties

are computed). Figure 5.10 shows the binary phase equilibria for this system in the

temperature range between 244–266 K. In the relatively high temperature range, the

difference in relative volatility is only about 12% for ethane-rich mixtures and nearly

zero for ethylene-rich mixtures. Using these data, we design a continuous distillation

column for a saturated liquid feed containing 50 mole % of ethylene. The target product


0 0.2 0.4 0.6 0.8 1x

C2H

4

, yC

2H

4

245

250

255

260

265

T [

K]

0 0.2 0.4 0.6 0.8 1

xC

2H

4

1.36

1.4

1.44

1.48

1.52

1.56

α TraPPE--UA

TraPPE--UA2

Figure 5.10: Binary ethane–ethylene phase behavior: temperature–composition diagram(bottom) and relative volatility–composition dependence (top) at p = 1.99± 0.01 MPafor TraPPE–UA2 models and at p = 2.39± 0.01 MPa for TraPPE–UA models.

purity is 95 mole % ethylene in the distillate and 5 mole % ethylene in the residue.

At a reflux ratio value of 1.2 times the minimum reflux required to achieved the target

purities, estimates using the TraPPE–UA and TraPPE–UA2 models require a total of

41 and 36 theoretical stages, respectively. The TraPPE–UA force field predicts 19 and

22 theoretical stages for the rectifying and the stripping sections of the distillation unit,

respectively, while the TraPPE–UA2 model predicts these numbers to be 19 and 17,

respectively. Since the difference in separation factors of the two force fields is more

pronounced for the ethane-rich mixtures, the column sizes only differ in the stripping

section. The TraPPE–UA model results in an over-design of the column by about 14 %

for this case, assuming that the TraPPE–UA2 model is exactly accurate in predicting


0 0.2 0.4 0.6 0.8 1x

C2H

4

, yC

2H

4

2600

2800

3000

3200

3400

p [

kP

a]

Mollerup [Experiment]

lEE

= 80 pm

lEE

= 130 pm

lEE

= 180 pm

Figure 5.11: Binary CO2–ethylene phase behavior: pressure–composition diagram atT = 263.15 K using three different ethylene models and the Lorentz–Berthelot combiningrules. Filled and open symbols represent the compositions of the liquid and vapor phases,respectively.The experimental data are taken from Mollerup. [168]

the experimental Txy diagram, an extrapolation from the predictive capabilities of this

model described earlier (see Figures 5.9 and 5.8). While the differences in the two models

may appear to be small, the results can be quite different in terms of distribution of

the stages within the rectifying and stripping sections, if the target product purity is

increased beyond 95%. Comparison of the data in Figures 5.9 and 5.8 also indicates that

the differences between TraPPE–UA2 and TraPPE–UA would be much more pronounced

for a distillation process performed at pressures lower than 100 kPa.

5.3.4 Binary ethylene/CO2 VLE

Separation of carbon dioxide and ethylene is important for industrial gas processing, and

the mixtures of these compounds are known to be highly non-ideal. [168] Since both these

molecules contain quadrupole moment as the highest term in their charge distribution,

their binary vapor–liquid equilibria may allow to accurately capture the quadrupolar

interactions for the ethylene model. Figure 5.11 shows the pxy diagram for ethylene/CO2


0 0.2 0.4 0.6 0.8 1x

C2H

4

, yC

2H

4

2800

3200

3600

4000

p [

kP

a]

0 0.2 0.4 0.6 0.8 1

xC

2H

4

0.5

1

1.5

2

2.5

α

Mollerup [Experiment]

Lorentz-Berthelot

Kong

Kong [LB for CO2--CO

2]

Waldman-Hagler

Figure 5.12: Binary CO2–ethylene phase behavior: pressure–composition diagram (bot-tom) and relative volatility–composition dependence (top) at 263.15 K using differentcombining rules for the LJ potential. Filled and open symbols represent the composi-tions of the liquid and vapor phases, respectively. The experimental data are taken fromMollerup. [168]

mixtures at 263.15 K using Lorentz–Berthelot combining rules. It can be seen that

although the pure component vapor pressures of both ethylene and CO2 are reasonably

accurate, none of the three ethylene models can capture the high-pressure azeotrope

for this system. This observation is in agreement with previous studies by by Weitz

and Potoff, where they tried a three-site point charge model of ethylene to mimic the

quadrupolar interactions. [146]

The Berthelot rule, that treats the unlike interaction strength (εij) as the geometric

mean of the two self-interaction strengths (εii and εjj), is known to overestimate the


εij parameter for atoms/groups/molecules with different sizes. [56] The effect of the com-

bining rule on the binary phase behavior of rare gases revealed the inadequacy of the

Lorentz–Berthelot combining rules and Kong rules were shown to be in better agreement

with experimental data. [169] Figure 5.12 shows the effect of combining rule on the binary

phase diagram of CO2 with ethylene. It is clear that Lorentz–Berthelot rule overesti-

mates the unlike interaction and therefore underestimates the mixture vapor pressure.

Both Waldman–Hagler and Kong combining rules use geometric mean for the quantity,

εσ6, instead of the geometric mean for ε alone, thereby allowing for different sizes of

the LJ sites to influence the strength of their interaction. Both these rules are able to

predict the high-pressure azeotrope of CO2 with ethylene, but the Kong rules yield pre-

dictions closer to the experimental data in terms of both, the azeotrope pressure and the

azeotrope composition. Since the TraPPE CO2 model, with two different LJ sites, was

parametrized using the Lorentz–Berthelot rules, [55] the pure-component CO2 pressures

are over-estimated when using the other two combining rules. When Lorentz–Berthelot

rules are employed for the CO2–CO2 interactions, and Kong rules are employed for the

ethylene–CO2 interactions, the pxy diagram is considerably improved in the CO2-rich

region. The maximum deviation in relative volatility is about 10, 10, and 60% for

Lorentz–Berthelot, Kong and Waldman–Hagler combining rules, respectively. It is im-

portant to note here that the binary ethane/ethylene VLE is not found to be influenced

by the combining rule since the σ values for these molecules are quite close (352.0 and

357.5 pm) as opposed to 280 and 305 pm for the carbon and oxygen sites of CO2, respec-

tively. Although the binary phase behavior improves considerably by the appropriate

choice of combining rules, the phase behavior is not very sensitive to the choice of lEE

(and hence the corresponding charge) for the ethylene model, and additional properties

will be required to select this parameter.

5.3.5 Binary ethane/CO2 VLE

Similar to CO2/ethylene, CO2/ethane mixtures are also of considerable interest in the

gas separations field. Fredenslund and Mollerup have experimentally investigated bi-

nary VLE of CO2 and ethane at temperatures of 223.15, 243.15, 263.15, 283.15, and

293.15 K. [170] At the four lower-temperature isotherms, the system exhibits a minimum-

boiling (maximum pressure) azeotrope. It is desirable to evaluate the performance of the


0 0.2 0.4 0.6 0.8 1x

C2H

6

, yC

2H

6

2000

2400

2800

3200

p [

kP

a]

Fredenslund & Mollerup [Expt.]

Simulation

0 0.2 0.4 0.6 0.8 1

xC

2H

6

0.4

0.8

1.2

1.6

2

2.4

α

Figure 5.13: Binary CO2–ethane phase behavior: pressure–composition diagram at T =263.15 K using TraPPE–UA2 ethane model and the Kong combining rules (CO2–CO2

interactions are modeled using the Lorentz–Berthelot combining rules). Filled and opensymbols represent the compositions of the liquid and vapor phases, respectively. Theexperimental data are taken from Fredenslund and Mollerup. [170]

TraPPE–UA2 ethane model for this binary mixture. As can be see from Figure 5.13,

the predicted isotherm and azeotropic composition are in very good agreement with

the experimental phase diagram. Most importantly, the relative volatilities, that depict

the extent of separation between the two compounds, agree extremely accurately with

experiments.

5.3.6 Binary H2O/ethane VLE

Culberson and McKetta measured the solubility of ethane in water over a wide temper-

ature range of 311–488 K up to pressures as high as 70 MPa. [171] The dependence of the


0 10 20 30 40 50 60 70p [MPa]

0.000

0.001

0.002

0.003

0.004

xC

2H

6

Culberson & McKettaLorentz--Berthelot [TIP4P]Kong [TIP4P]

Waldman--Hagler [TIP4P]

0 10 20 30 40 50 60 70p [MPa]

0.000

0.001

0.002

0.003

0.004

xC

2H

6

Kong [TIP4P/2005]

Waldman--Hagler [TIP4P/2005]

Figure 5.14: The solubility of ethane in water versus pressure at T = 444.26 K forTraPPE–UA2 model of ethane and different combinations of H2O models and combiningrules. The experimental data are taken from Culberson and McKetta. [171]

ethane solubility in water with respect to temperature is quite complex and depends on

the pressure range. At constant pressures below 70 MPa, on increasing the temperature,

solubility first decreases, passes through a minimum, and then increases again. This

behavior may be attributed to the complex dependence of hydrogen bond formation in

water with respect to temperature. As a test case, the solubility of the TraPPE–UA2

ethane model in water was investigated using different combining rules and water models

(see Figure 5.14). Compared to the TIP4P/2005 model, the TIP4P water model yields

a significantly better agreement for the ethane solubility. Combining rules have a small

effect in case of the ethane/H2O binary mixtures due to relatively smaller difference

in the LJ diameters of ethane and water (σCC = 352.0 pm vs. σOO = 315 pm) com-

pared to the difference for ethylene (σCC = 357.5 pm) versus CO2 (σOO = 305 pm and

σCC = 280 pm). Nonetheless, the Kong rules lead to the most accurate predictions for

solubility of ethane in water modeled by the TIP4P force field.


5 10 15 20 25 30p [MPa]

0.000

0.002

0.004

0.006

0.008

xC

2H

4

lEE

= 0 pm

lEE

= 80 pm

lEE

= 130 pm

lEE

= 180 pm

5 10 15 20 25 30p [MPa]

0.000

0.002

0.004

0.006

0.008

xC

2H

4

Anthony & McKetta

Figure 5.15: The solubility of ethylene in water versus pressure at T = 411 K for differentethylene models and TIP4P model for H2O. Open symbols are results using the Kongcombining rule and corresponding filled symbols show results using the Waldman–Haglercombining rule. The experimental data are taken from Anthony and McKetta. [172]

5.3.7 Binary H2O/ethylene VLE

Figure 5.15 compares the solubility of different ethylene models in water, using two

different combining rules, to the experimental measurements at 411 K. [172] The solubility

prediction for the three-site ethylene model (lEE = 0) is quite poor, and practically does

not improve by increasing lEE to 80 pm. Depending on the choice of combining rule, an

optimum exists for the lEE parameter, that accurately predicts the solubility of ethylene

in water. This optimum is at 130 pm using the Kong rules and greater than 180 pm

for the Waldman–Hagler rules. Note that very high values of lEE can lead to unstable

models due to the unprotected negative charges on these sites forming an unphysically

strong bond with the unprotected positive charges on hydrogens in water. Moreover,

since the Kong rules were shown to perform better for CO2/ ethylene and ethane/water

systems, they appear to be the most appropriate choice here as well.

As an additional check for the choice of the lEE parameter, the structure for the


0.41 0.32 0.230.47

qC [e]

0.0

7.5

15.0

22.5

30.0

|E| [

kJ/

mol]

80 130 1800lEE

[pm]

250

300

350

400

450

r H2O

--C

2H

4

[p

m]

Peterson & Klemperer

ethylene/TIP4P

ethylene/TIP4P-2005

Figure 5.16: Distance between the center of masses of H2O and ethylene (left axis) andthe binding energy of the dimer (right axis) for the different ethylene and water models.The x-axis at the bottom shows the distance between the π electron sites and the oneat the top shows the corresponding optimized charge. The dashed line indicates thedistance deduced from spectroscopic measurements. [173]

water/ethylene dimer is optimized at a low temperature of 0.01 K (see Figure 5.16). The

distance between the centers of mass of ethylene and water decreases as lEE is increased,

and is accompanied with an increase in the binding energy. Rotational spectroscopy of

the C2H4–H2O dimer using the molecular beam electric resonance technique showed the

distance between the centers of masses of these two molecules to be 341.3 pm. [173,174]

While this may indicate that lEE < 80 pm may lead to accurate match for this property,

as mentioned earlier, smaller charge–charge separation increases the cost of Ewald sum

convergence. Moreover, since increasing lEE from 0.8 to 130 pm does not appreciably

alter the distance between the centers of mass, but significantly improves the solubility

in liquid water, it can be inferred that 130 pm is the better choice. It can also be seen

that there is practically no difference in the dimer distances and energies for the TIP4P

and TIP4P/2005 water models. We conclude that lEE = 130 pm is the best choice, and

with this, selection of all five parameters for the ethylene model is complete.


The TraPPE–UA2 ethane and ethylene models developed in this work are very ac-

curate for the vapor pressures, liquid densities at T < 0.8Tc, and the mixture separation

factors. Although the new models are reasonably accurate for the critical properties,

the deviations in liquid and vapor densities at very high reduced temperatures are in-

triguing. It is possible that ignoring the higher-order dispersion terms, such as r−8 and

r−10, and using only a lumped dispersion term (r−6) amounts to interactions that are

slightly too long-ranged and respond too weakly to density decreases. This may result

in an over-estimation of the cohesive energy, that in turn overstabilizes the two-phase

region at higher temperatures. Alternatively, the three-body and higher-order disper-

sion terms, [56] that are not included in the majority of commonly used force fields in the

literature (including TraPPE–UA2), may be repulsive for these compounds. Explicitly

including many-body induction terms would likely also lead to additional weakening of

the cohesive interactions as the critical point is approached. It would certainly be pos-

sible to develop even more accurate force fields that capture these additional physical

phenomena, but only at the expense of significantly increased costs for the potential

energy calculations.

5.4 Conclusion

An improved version of the Transferable Potentials for Phase Equilibria – United Atom

force field has been developed for ethane and ethylene, with a view to improving the

accuracy of the models, without significant increase in the simulation expense. The

recommended force field parameters are listed in Table 5.1.

Ethane is described by a two-site model with the distance between the sites being

treated as a parameter in the force field fitting. The new force field accurately reproduces

the temperature dependence of the saturation vapor pressure, along with other properties

such as critical point and liquid densities. The ethylene model comprises of four sites,

including two LJ interaction sites with a partial positive charge and two compensating

negative partial charges, mimicking the π-bonded electrons in ethylene, placed above

and below the line joining the LJ centers. For the ethylene model, in addition to the

unary VLE, binary VLE with ethane, CO2, and H2O are also included in determining

the choice of parameters.


The combining rule has a significant effect on the binary phase equilibria for molecules

with very different LJ diameters, but not for the ethane/ethylene mixture. The Kong

rules are found to perform the best among the three combining rules assessed in this

work and future development, of the TraPPE force field, will consider this aspect. It is

important to note here that the models within TraPPE–small will perform better using

the Lorentz–Berthelot rule, but interactions of these molecules with TraPPE–UA2 is

described better by the Kong rules. It is also worth noting that mixtures of TraPPE–UA2

with TraPPE–UA may result in relatively poor prediction of separation performance.

Mixtures of TraPPE–UA2 with TraPPE–small is recommended, for instance, mixtures

simulated using the TraPPE model for H2S [37] or CO2[55] with TraPPE–UA2 will lead

to a higher accuracy of predictions.

The new ethylene model, that efficiently and explicitly accounts for the complex

quadrupolar interactions and effective many-body polarization with diverse molecules,

opens up the possibility to improve predictions for ethylene in polar environments, such

as cationic zeolites, metal–organic frameworks, and ionic liquids.

Chapter 6

C2 Adsorption in Zeolites: In Silico

Screening and Sensitivity to

Molecular Models

Reproduced from M. S. Shah, E. O. Fetisov, M. Tsapatsis, and J. I. Siepmann, Mol. Syst.

Des. Eng. 2018 with permission from the Royal Society of Chemistry. http://pubs.

rsc.org/en/content/articlelanding/2018/me/c8me00004b/unauth#!divAbstract

6.1 Introduction

If an adsorbent selectively adsorbs the valuable component (ethylene in this case), re-

covering this component in a high-purity form is challenging because the unadsorbed

ethane in the interstitial spaces will contaminate the high-purity ethylene during des-

orption. [12] Adsorbents that selectively adsorb ethane instead of ethylene can yield a

highly pure ethylene stream if the column is operated in the breakthrough mode, in-

stead of a pressure- or temperature-swing mode. Gucuyener et al. first developed an

ethane-selective MOF, ZIF-7, that operates via a gate-opening mechanism. [21] Liao et al.

synthesized a Zn-based azolate framework (MAF-49) that binds preferentially to ethane

(−60 kJ/mol) over ethylene (−50 kJ/mol) due to strong C–H· · ·N hydrogen bonds with

C2H6 instead of the polar C2H4. [22] While MAF-49 binds preferentially to ethane, it

103

http://pubs.rsc.org/en/content/articlelanding/2018/me/c8me00004b/unauth#!divAbstract

http://pubs.rsc.org/en/content/articlelanding/2018/me/c8me00004b/unauth#!divAbstract

Chapter 6: C2 Adsorption in Zeolites: In Silico Screening and Sensitivity to MolecularModels 104

suffers from high energy of regeneration. On the contrary, the adsorption enthalpy of

ZIF-7 is only about −30 kJ/mol.

Zeolite frameworks in their all-silica or aluminophosphate form constitute a less polar

class of potentially ethane-selective materials. Siliceous small pore eight-ring zeolites, ar-

guably the most size-/shape- selective molecular sieves, such as DDR, [175] CHA, [176,177]

LTA, [178] and AEI [177] have been investigated for selective ethane adsorption. While

some of these zeolites such as ITE, DDR, and CHA favor transport of propylene over

propane with respective diffusion selectivities of 690, 12000, and 46000, [176] differenti-

ating C2H4 from C2H6 using siliceous zeolites has seen limited success, both kinetically

and thermodynamically. [175–177,179,180] The database of the International Zeolite Asso-

ciation (IZA) comprises of 234 unique zeolite framework topologies. [181] In 2012, Kim

et al. screened such frameworks (171 from the IZA database [181] and 30,000 from the

hypothetical zeolite database [182]) for adsorptive separation of ethane from ethylene at

T = 300 K and p = 1 bar. [23]

We have recently developed a new version of the transferable potentials for phase

equilibria molecular models, TraPPE–UA2, for ethane and ethylene. [183] These models

account for a better description of the molecular shapes and of the first-order electrostatic

interactions in the case of ethylene. The improved performance of these new models can

be judged from their accurate pure and mixture vapor pressures and separation factors

for ethane/ethylene, ethane/water, ethylene/water, ethane/CO2, and ethylene/CO2 sys-

tems. Using these improved molecular models, we revisit the problem of screening of

the IZA database for C2 separation and also present a systematic study on sensitivity

of in silico predictions to the choice of molecular models.

6.2 Simulation Details

Monte Carlo simulations in the isobaric–isothermal (NpT ) version of the Gibbs ensem-

ble [31] are used to compute the binary C2H4/C2H6 adsorption isotherms in 214 all-silica

frameworks at T = 300 K and p = 20 bar and unary isotherms at T = 303 K in select

all-silica frameworks. For the overall composition of zC2H4 = 0.5, both TraPPE–UA and

TraPPE–UA2 force fields are used to perform the screening. For the top six ethylene-

selective (DFT, ACO, AWO, UEI, APD, and SBN) and the top four ethane-selective


(NAT, JRY, ITW, and RRO)framework types, additional conditions (T = 300 K,

p = 20 bar, zF = 0.9 and T = 400 K, p = 50 bar, zF = 0.5) are investigated. For

every mole of silicon atoms in the two-phase system, one mole of gas mixture at overall

composition of zC2H4 is contacted.

Since the flexibility of the different framework types can be quite different depending

on its local bond structure, the zeolite frameworks are treated to be rigid for the purposes

of screening the database. For some of the top-performig structures, computationally

expensive ab initio calculations with framework flexibility are performed to understand

the extent of validity of this approximation. Out of the 234 idealized all-silica structures

from the IZA–SC database, [181] 214 charge-neutral structures are considered for this

screening study. Sorbate–sorbent interactions are pretabulated with a grid spacing of

approximately 0.2 Å and interpolated during the simulation for any position of the

guest species in the zeolite phase. It is known that some of the framework types contain

inaccessible cages due to narrow pore windows. For the screening study, these cages

were not blocked apriori and Monte Carlo simulations may predict an artificially high

loading for some of these cases (discussed below).

The non-bonded interactions are modeled using a pairwise-additive potential con-

sisting of Lennard–Jones (LJ) 12–6 and Coulomb terms. Different versions of the

Transferable Potentials for Phase Equilibria force field are used for C2H6 (TraPPE–

UA [34], TraPPE–UA2 [183], and TraPPE–EH [35]), C2H4 (TraPPE–UA [143] and TraPPE–

UA2 [183]) and zeolites (TraPPE-zeo [36]). The standard Lorentz–Berthelot combining

rules are used to determine the LJ parameters for all unlike interactions. [56]

For the pure-component adsorption of ethane and ethylene, each of the eight in-

dependent simulation trajectories is equilibrated for at least 10000 Monte Carlo cycles

(MCCs), followed by a production period of at least 25000 MCCs and uncertainties are

estimated as the standard error of the mean for these independent simulations. An equi-

libration period of at least 25000 MCCs is used for the binary systems in the screening

study, which is followed by a production period of 100000 MCCs.

Potentials of mean force (PMFs) for diffusion of ethane and ethylene in DFT, ACO,

and UEI frameworks are obtained from first principles molecular dynamics (FPMD)

simulations in the canonical ensemble using umbrella sampling. Each system is modeled

in CP2K software suite [184] with the PBE exchange–correlation functional, [185] GTH


pseudopotentials, [186] the MOLOPT double-zeta basis set, [187] a 400 Ry cutoff for the

auxiliary plane wave basis, and Grimme D3 dispersion correction. [188] The simulated

system consists of 3×3×1 unit cells for ACO, 3×3×2 unit cells for DFT, and 1×2×1

unit cells for UEI. The temperature is set to 303 K using Nosé–Hoover [189,190] chain [191]

thermostats, and the time step is set to 0.5 fs. Harmonic umbrella potentials of the form

V (r) = (1/2)k(r0 − r)2 with k = 400 kJ/mol/Å2 are employed to restrain the center-

of-mass (COM) of the sorbates and the weighed histogram analysis method (WHAM)

is used to compute free energies [192]. PMFs are expressed as the function of the COM

coordinate along the diffusion-limiting channel (c direction for DFT and ACO and b

direction for UEI) and ξ = 0 or 1 correspond to the channel intersections. For each

channel, 33 equally spaced umbrella windows are used to constrain the sorbates. Each

configuration is equilibrated for 2 ps and at least 4 ps of production were used for the

analysis.


Before performing a screening of binary mixtures of ethane and ethylene in all the frame-

works in the IZA database, we validate our models using the available pure-component

experimental data in some of the all-silica zeolites. Figure 6.1 shows the adsorption

isotherms of ethane and ethylene in MFI-type zeolite. For the TraPPE–UA2 force

field, data for three different MFI structures (MFI-0, [181] MFI-1, [110] and MFI-2 [193])

is presented for comparison. In the low-pressure part of the isotherms, there is a quan-

titative agreement between the different TraPPE models and the experimental data.

The experimental data at pressures over 0.1 bar show a significant variation. [10,179] The

near-saturation isotherm predictions using the different TraPPE models (UA and UA2

for ethylene and UA, UA2, and EH for ethane) fall within the experimental bounds.

While the relative difference in loading for the different MFI structures may not be very

significant in the saturated region, the low-pressure data can differ appreciably. Similar

to MFI, there is a very good agreement between the predicted and the experimental ad-

sorption isotherms for CHA, DDR, AEI, and STT (see Figures S1–S4 in the supporting

information1). No significant differences in predictions between the UA and UA2 models1http://www.rsc.org/suppdata/c8/me/c8me00004b/c8me00004b1.pdf

http://www.rsc.org/suppdata/c8/me/c8me00004b/c8me00004b1.pdf


0

4

8

12

16

Q [

mole

cule

s/u

c]

Choudhary & Mayadevi (305 K)

Stach et al.

Song et al.

EH (MFI-1)

UA (MFI-1)

UA2 (MFI-1)

UA2 (MFI-2)

UA2 (MFI-0)

10-3

10-2

10-1

100

101

102

p [bar]

0

4

8

12

16

Q [

mole

cule

s/uc]

Choudhary & Mayadevi (306 K)

Stach et al.

UA (MFI-1)

UA2 (MFI-1)

UA2 (MFI-2)

UA2 (MFI-0)

Ethane

Ethylene

Figure 6.1: Unary adsorption isotherms of C2H6 (top) and C2H4 (bottom) at T = 303 Kin MFI using the TraPPE–UA, TraPPE–UA2, and TraPPE–EH models; experimentaldata are from Choudhary and Mayadevi, [179] Stach et al., [10] and Song et al. [180]

for ethane and ethylene are observed for these five frameworks.

High capacity and high selectivity are two essential criteria for an adsorbent to

energy-efficiently run separation processes. We define the performance measure of each

adsorbent to be a product of the loading of the strongly adsorbing species (Q) and loga-

rithm of the selectivity towards this species (S). [194] Figure 6.2 presents the performance

criteria of zeolitic frameworks for the separation of ethane and ethylene at T = 300 K

and p = 20 bar with an equimolar starting mixture of ethane and ethylene. Selectivity is

defined as, S = [xi/(1−xi)]/[yi/(1− yi)], where i is the more strongly adsorbing species


1 2 3 4 5 10 20

0

3

6

9

12

15

18

Q *

ln

(S)

[mm

ol/

g]

SB

N

AP

D

RR

O

DF

T

AC

O

AW

O

UE

I

NA

T

JRY

ITW

T = 300 K; p = 20 bar; zF = 0.5

T = 300 K; p = 20 bar; zF = 0.9

T = 400 K; p = 50 bar; zF = 0.5

20 30 40 50 100 200 250performance ranking

0.0

0.5

1.0

1.5

Q *

ln

(S)

[mm

ol/

g]

Figure 6.2: Performance criteria (Q∗ ln(S)) for the separation of a 50:50 binary mixtureof ethane and ethylene at T = 300 K and p = 20 bar, using zeolitic framework types fromthe IZA–SC database. The ranking of the framework as per the performance criteria isshown on the x axis (ranks 1–20 (top) and ranks 20–214 (bottom)). Frameworks withS ≥ 3 and Q ≥ 1 mmol/g are shown on the plot with their three-letter IZA code. For theten selective frameworks, the performance criteria at two other conditions (T = 300 K,p = 20 bar, zF = 0.9 and T = 400 K, p = 50 bar, zF = 0.5) are shown as orangetriangles and green squares, respectively. Frameworks labelled in magenta and green areethylene- and ethane-selective, respectively.

and x and y are mole fractions in the zeolite and the gas phases, respectively. The top

panel highlights the top-20 high-performing framework types, while the bottom panel

shows the data for frameworks with ranking between 20 and 214. The TraPPE–UA2

force field predicts that there are six and four ethylene- and ethane-selective frameworks,

respectively, that have S ≥ 3 and Q ≥ 1 mmol/g. None of these ten top-performing


structures suffer from the presence of inaccessible cages. The IZA–SC database suggests

the value of “maximum diameter of a sphere that can diffuse along” for DDR framework

to be 3.65 Å. [181] These values for ACO, UEI, DFT, AWO, APD, and SBN are 3.56, 3.77,

3.65, 3.67, 3.63, and 3.8 Å, respectively. Similarly, for the ethane-selective frameworks,

NAT, JRY, ITW, and RRO, the values of the “maximum diameter of a sphere that can

diffuse along" are 4.38, 4.4, 3.95, and 4.09, respectively. Clearly, all these values are

either higher or very close to the value for DDR, a framework in which both ethane and

ethylene adsorb experimentally.

Screening using the TraPPE–UA force field showed ethylene selectivities of 2.8, 3.0,

1.8, 1.4, 5.7, and 4.3 for DFT, ACO, AWO, UEI, APD, and SBN, respectively; the

respective ethylene loadings are 2.6, 1.3, 1.6, 1.4, 2.1, and 3.0 mmol/g. Therefore, only

three (ACO, APD, and SBN) out of the six frameworks satisfy the selection criteria for

ethylene-selective frameworks and none are selective towards ethane when TraPPE–UA

is used to screen the IZA database. This suggests that although both UA and UA2 force

fields yield good agreement with available experimental isotherms for several zeolites,

the predictions for the entire database show important differences.

For the 10 top-ranking structures, performance is also assessed at two different feed

conditions (T = 300 K, p = 20 bar, zF = 0.9 and T = 400 K, p = 50 bar, zF = 0.5). At

zF = 0.9, the performance for ethylene-selective structures improve while that for ethane-

selective structure deteriorates. This is because the loading of ethylene increases when

the feed concentration of ethylene is increased while that for ethane shows a decrease

and also because composition has only a mild influence on the selectivity. At T = 400 K,

the performance criteria for all the structures show a significant deterioration because

although the selectivity is not much affected, the loading of the adsorbate decreases

tremendously at this high temperature even if a higher feed pressure of 50 bar is applied.

Therefore, although the adsorption process may not be feasible at T = 400 K, this

temperature is more than sufficient for regeneration of the adsorbent bed. Performance

of the top-ranking structures that emerged in this screening study is discussed below.

Presence of defects such as silanol groups or cation impurities can impact the po-

larity of a zeolite framework. These polar impurities can influence the adsorption of

ethylene due to stronger binding of the π-bonded electrons with the cations or protons

and may further enhance the selectivity towards ethylene. For the screening study, this


10-2

10-1

100

101

102

103

p [bar]

0

0.5

1

1.5

2

Q [

mole

cule

s/uc]

ethane-UA

ethane-UA2

ethane-EH

ethylene-UA

ethylene-UA2

Figure 6.3: Unary adsorption isotherms of C2H4 and C2H6 at T = 303 K in DFT usingvarious TraPPE models.

issue will be considerably more forgiving for the ethylene-selective frameworks, but may

significantly reduce the selectivity towards ethane. In addition to factors such as force

field parameters and structural sensitivity, presence of defects can add to the uncertainty

of predictive modeling. Although somewhat arbitrarily picked in our study, computa-

tionally predicted structures with S ≤ 3, do not seem to be very promising targets for

further investigation. Note that the earlier screening study for C2 separation using all-

silica zeolite frameworks of the IZA–SC database found the highest selectivity to be only

2.9 (for the SOF framework type).

Figure 6.3 shows the pure-component adsorption isotherms of ethane and ethylene

in the DFT-type zeolite. Both UA and UA2 force fields for ethylene yield a very similar

adsorption isotherm. The large differences in the values of binary selectivity predicted by

the two models (2.8 and 41) can be attributed to the differences in the pure-component

isotherms of ethane. Using the model TraPPE–UA, ethane has the same saturation

loading as ethylene. Contrary to this, TraPPE–UA2 and TraPPE–EH predict negligi-

ble adsorption below p = 10 bar and only about 20% of the TraPPE–UA loading at

100 bar. The TraPPE–UA2 ethane model, very similar to the TraPPE–EH model, uses

a slightly elongated representation of ethane and this small variation in size may become

a determining factor as to whether or not it can pack well in the zeolite. The predicted

adsorption energy of ethane at Q = 0.4 molecules/uc for all the three TraPPE models


0.0 0.2 0.4 0.6 0.8 1.0ξ

0

10

20

30

40

∆G

[kJ/

mol]

0

10

20

30

40

∆G

[kJ/

mol]

0

10

20

30

40

∆G

[kJ/

mol]

ACO

DFT

UEI

Figure 6.4: Potentials of mean force for ethane and ethylene (represented by dashed andsolid lines, respectively) in ACO, DFT, and UEI zeolites. ξ = 0 and 1 correspond to thestart and end of one unit cell along the channel dimension.

(UA, UA2, and EH) is in the range of 21–22 kJ/mol. This confirms that the differences

in the adsorption isotherms predicted by the three models is mainly because of better

packing of the UA model as opposed to the UA2 and the EH models. These results

show how choice of force fields can significantly impact mixture predictions in certain

zeolites. Similar results are reported for the ACO and UEI frameworks in the supporting

information (see Figure S5).


DFT, ACO, and UEI are all eight-membered ring framework types with maximum

pore-opening diameter in the range of 3.5–4 Å. Since these dimensions are very similar to

the short dimension of both ethane and ethylene molecules, flexibility of the framework

may have a significant impact on the accessibility of the favorable adsorption sites. In

view of this, we calculate the potentials of mean force (PMFs) of ethane and ethylene

along channels of the DFT, ACO, and UEI frameworks from first principles molecular

dynamics simulations in the canonical ensemble using umbrella sampling. The DFT

framework type has a channel along the c direction; ACO is three-dimensionally sym-

metric with identical channels along a, b, and c directions; and UEI has a channel along

the b direction. Figure 6.42 shows PMFs for each of these zeolites along a unit cell in the

direction of the channel. It can be seen that in spite of the flexibility of the framework,

the energy barriers range between 25-45 kJ/mol. These results suggest that transport

in these materials may have an impact on the overall selectivity. ACO has a slightly

higher barrier for ethane compared to ethylene, UEI shows very similar barrier heights

for both, and DFT has higher barriers for ethylene compared to ethane. Therefore,

it is possible that the selectivity towards ethylene in a real adsorption unit may be en-

hanced for ACO, unaffected for UEI, and degraded for DFT. Nevertheless, these are very

promising structures with a high ethylene selectivity and constitute useful candidates

for future experimental investigation. None of these structures have yet been reported

to be synthesized in an all-silica composition.

It can be seen from Figure 6.2 that the TraPPE–UA2 force field yields four ethane-

selective frameworks (NAT, JRY, ITW, and RRO) with S ≥ 3 and Q ≥ 1 mmol/g.

These frameworks have larger pore-opening diameters (4–4.5 Å) and therefore unlike

the ethylene-selective frameworks, accessibility of the favorable sites is not an issue (also

evident from negligible variations in number density along the length of the channel).

In contrast, the screening with the TraPPE–UA force field did not yield any framework

with S ≥ 3 towards ethane. The SOF structure, that showed the highest selectivity of

2.9 towards ethane in the earlier screening study, [23] shows a selectivity of 1.3 towards

ethane and 1.2 towards ethylene using the TraPPE–UA and the TraPPE–UA2 force

fields, respectively. Different overall pressure of adsorption (20 bar versus 1 bar) may2The data shown in Figure 6.4 have been calculated by Evgenii O. Fetisov in the Siepmann Group

at University of Minnesota.


10-2

10-1

100

101

102

p [bar]

0

1

2

3

4

Q [

mo

lecu

les/

uc]

ethane-EH (ITW-1)

ethane-UA (ITW-1)

ethane-UA2 (ITW-1)

ethane-UA2 (ITW-0)

ethylene (Olson et al.)

ethylene-UA (ITW-1)

ethylene-UA2 (ITW-1)

ethylene-UA2 (ITW-0)

Figure 6.5: Unary adsorption isotherms of C2H4 and C2H6 at T = 303 K in ITW usingvarious TraPPE models; experimental data for ethylene are from Olson et al. [195]

be part of the reason for these differences. However, more importantly, while these may

appear to be significant differences in selectivity values, it should be mentioned here that

for selectivities close to unity, small differences in force fields may result in very different

selectivity values and these values may be considered to be within the noise of uncertainty

in molecular models. For framework type DFT at 300 K and 20 bar, the ethylene

selectivity values computed using the TraPPE–UA2, TraPPE–UA, and the force field

used by Kim et al. [23] are 41, 2.8, and 0.6, respectively. It is important to emphasize here

that the significant differences in prediction using the TraPPE–UA2 models compared to

both, the TraPPE–UA models and the models used in earlier screening study, [23] can be

mainly attributed to the differences in shape of the molecules more than the differences in

the strength of interaction with the all-silica zeolite. This is a very important finding that

should be considered in future computational studies investigating adsorption/transport

in microporous materials with pore sizes very close to molecular dimensions.


in ITW zeolite. Note that there are two different structures of ITW that are used

to compute the pure-component isotherms: ITW-0 and ITW-1. ITW-0 is the energy-

minimized pure-silica structure reported in the IZA–SC database, [181] while ITW-1 is the

calcined pure-silica structure (ITQ-12). [196] It can be seen that the ethane and ethylene


10-2

10-1

100

101

102

p [bar]

0

0.5

1

1.5

2

2.5

Q [

mole

cule

s/uc]

ethane (Pham & Lobo)

ethane-EH (RRO-1)

ethane-UA (RRO-1)

ethane-UA2 (RRO-1)

ethane-UA2 (RRO-0)

ethylene (Pham & Lobo)

ethylene-UA (RRO-1)

ethylene-UA2 (RRO-1)

ethylene-UA2 (RRO-0)

Figure 6.6: Unary adsorption isotherms of C2H4 and C2H6 at T = 303 K in RRO usingvarious TraPPE models; experimental data are from Pham and Lobo. [177]

isotherms for the ITW-1 structure are almost identical, while the isotherms for the ITW-0

structure show a higher affinity and saturation capacity for ethane compared to ethylene.

For the screening study, XXX-0 structure was used for each framework type and this

explains the selectivity observed for the ITW-0 structure. The limited experimental

data for ethylene adsorption in ITW are in better agreement with the simulated data for

the ITW-1 structure, suggesting that this may be the more probable structure during

experimental measurements and therefore further implying that ITW is unlikely to be

selective for adsorptive separation of ethane and ethylene. Nonetheless, these data show

the significant importance of the zeolite structures on the prediction of adsorption and

separation performance. Future screening studies, specially when separation factors are

not very high (S ≤ 10) should consider sensitivity to the structural variations of a

zeolite framework type. The isotherms for TraPPE–UA ethane and ethylene are almost

identical, thus explaining no selectivity using the UA force field. The ethane isotherm

using the TraPPE–EH force field is shifted to significantly higher pressures compared to

that using the UA2 force field. This has been observed also for RRO (discussed below)

and the ethylene-selective frameworks such as DFT, ACO, and UEI.


in RRO zeolite. The experimental isotherms for these two species are almost identical,

suggesting no selectivity towards either species. The isotherm for TraPPE–UA2 ethane


in RRO-1 (RUB-41 [197]) is in close agreement with the experimental measurements for

this framework. However, TraPPE–UA2 seems to significantly over-predict the uptake

pressure of ethylene. It is not clear why only one out of the seven all-silica zeolites (MFI,

CHA, DDR, STT, AEI, ITW, and RRO) yields a poor agreement for the TraPPE–UA2

model with the experimental data for ethylene. Since the 29Si NMR for the RUB-41

material shows negligible contribution from the Q3 peaks, [177] it is unlikely that there is

an error in the experimental measurements due to a poorly synthesized material. Once

again, since the isotherms are very sensitive to small structural variations of a particular

framework (see RRO-0 versus RRO-1), there is a chance that a slightly different RRO

structure may yield a very good agreement with the experimental ethylene isotherm.

Similar to RRO, the other two ethane-selective frameworks (NAT and JRY) also show the

TraPPE–UA2 prediction of ethylene isotherm to be shifted to a higher pressure compared

to the ethane isotherm (see Figure S6). These two zeolites have not yet been reported

to be synthesized in their all-silica forms and may constitute potential candidates for

future experimental investigation. Another important point to note here is that although

TraPPE–EH is a more complex and presumably more accurate description of ethane, it

need not necessarily perform better in predicting adsorption in confined materials.

6.4 Conclusion

In conclusion, we have used a more reliable set of molecular models for ethane and ethy-

lene to screen the IZA database of zeolitic structures. It is clear that the adsorption

and separation predictions from computational techniques can be highly sensitive to

the molecular models that are employed for the simulations. We have identified some

promising all-silica zeolite structures for adsorptive separation of ethane and ethylene.

DFT, ACO, AWO, UEI, APD, and SBN frameworks are predicted to be selective towards

ethylene and computation of diffusion energy barriers for some of these frameworks show

that transport may play a significant role in affecting the breakthrough performance of

these materials. Nonetheless, all-silica synthesis of these framework has not yet been re-

ported and future experimental investigations on these framework types will help further

research in this area. Similarly, all-silica NAT and JRY frameworks will be interesting

synthesis targets for developing ethane-selective materials.

Chapter 7

Zeolite Synthesis: Literature Survey

and Potential Future Targets

7.1 Introduction

Zeolites are microporous aluminosilicates with pores of molecular dimensions (3–20Å).

Many are found as natural minerals, but it is the synthetic variants that largely consti-

tute the commercial catalysts and sorbents. Since the early 1980s, several new zeotypes

(zeolite-like materials), that contain elements other than silicon and aluminum, have

been synthesized. Wilson et al. proposed a new class of materials, the aluminophos-

phates (AlPOs), composed of alternating tetrahedra of aluminum (AlO4) and phos-

phorus (PO4). [198,199] These were the first class of microporous framework oxides that

were synthesized without silica. Subsequently, another class of materials, the silicoa-

luminophosphates (SAPOs), intermediate between zeolite and aluminophosphates, was

also synthesized. [200]

Baerlocher et al. remarked that “zeolites and zeolite-like materials do not comprise an

easily definable family of crystalline solids”. [201] Framework density (number of tetrahe-

drally coordinated framework atoms per unit volume) is used as a criterion to distinguish

zeolites from the denser tectosilicates (mineral group with three-dimensionally connected

silicate tetrahedra); zeolites possess a maximum framework density of 19–21 Å. The

database of the Structure Commission of the International Zeolite Association (IZA–

SC) has approved and assigned a three-letter code to 235 unique zeolite (and zeotype)

116

Chapter 7: Zeolite Synthesis: Literature Survey and Potential Future Targets 117

framework types as of February 2018; [181] this number was 176 in 2007, 133 in 2001, and

a mere 27 in 1970. [201] This slow but steady increase in the number of zeolite framework

types is indicative of not only the large quantum of research effort to find new zeolites

structures for existing and new applications, but also the relative difficulty involved in

synthesizing new structures compared to some of the other classes of crystalline materials

such as metal–organic frameworks.

Typically, zeolites and zeotypes are synthesized from a reactive gel in alkaline (hy-

droxide) media under hydrothermal conditions at temperatures between 80−200◦C. [101,202]

Low-pH synthesis based on fluoride-containing reactive gels has also been widely and suc-

cessfully implemented in many cases. [203–208] In the early days, zeolites were synthesized

using only inorganic reactants. It was only in 1961, that organics such as quaternary

ammonium salts were used for the first time in the reaction gel. [209] These organics are

commonly referred to as structure-directing agents (SDAs) or templates since the zeolite

framework crystallizes enveloping these organic molecules, sometimes very closely that

the pores and channels of the framework take shape of the organic molecule. Several

synthetic variables such as source of the ingredients, composition of the reactive gel,

presence of various organics as SDAs or templates, time for crystallization, and synthe-

sis temperature govern the final phase (and the impurities) that will be present in the

synthesis product. There is significant effort in the field to understand the mechanisms

that govern zeolite formation and methods to regulate phase selectivity. However, due

to the vast range of variables and structural and compositional space of this class of

materials, a complete understanding enabling a highly rational synthesis of the desired

zeolites still remains an area of open research. [210–212]

7.2 All-Silica Zeolites

In this thesis, it is proposed and is proved by molecular simulation that some of the

hydrophobic all-silica zeolites are able to selectively separate H2S from sour natural gas

mixtures and ethane from ethylene. In this section, a summary of the zeolites that

have been reported in the literature to have been synthesized in their all-silica forms is

presented.

The SDA molecules described earlier also play the role of charge-balancing cations


Table 7.1: Framework types with all-silica synthesis (largest ring being eight- or nine-membered).

framework type material name reference

CDO CDS-1 Ref. 221CHA pure silica chabazite Ref. 106DDR pure silica DDR Ref. 222,223ETL EU-12 Ref. 224IFY ITQ-50 Ref. 225IHW ITQ-32 Ref. 226ITE ITQ-3 Ref. 227ITW ITQ-12 Ref. 228LTA ITQ-29 Ref. 229MTF MCM-35 Ref. 230RTE RUB-3 Ref. 231RTH RUB-13 Ref. 232,233SAS SSZ-73 Ref. 234STT SSZ-23 Ref. 235

similar to alkali cations such as Na+, K+, and Li+ in a purely inorganic synthesis. Since

these organic cations are typically much larger in size compared to the inorganic alkali

cations, the frameworks that crystallize can accommodate much lower charge density,

resulting in materials with higher Si/Al ratios (since it is the alumina tetrahedra that

imparts the anionic charge to the framework). The slower growth rates for high-silica ma-

terials demand longer synthesis durations and temperatures compared to their low-silica

counterparts. [202] As an advancement to the conventional hydrothermal synthesis, new

techniques involving ionic liquids as solvents and SDAs, known as ionothermal synthe-

sis, [213,214] have emerged. This technique have been able to synthesize some of the zeolites

such as MOR [215] and MRE [216] in their hitherto unknown pure-silica forms. There has

been significant effort in the literature to synthesize high-silica and pure-silica zeolites

and further information can be found in extensive reviews on the subjects. [205,217–220]

Table 7.1 summarizes the 14 small-pore (eight- or nine- membered rings in the lim-

iting pore) zeolite framework types that have been reported to be synthesized in their

pure-silica forms. Similarly, Table 7.2 summarizes the 32 framework types with limiting

pore openings having ten-membered or larger rings. While all-silica material ensures low


Table 7.2: Framework types with all-silica synthesis (ten-membered rings or larger).

framework type material name reference

AFI SSZ-24 Ref. 236ATS silica-SSZ-55 Ref. 237BEA pure silica beta Ref. 238BEC ITQ-14 Ref. 239CFI CIT-5 Ref. 240CSV CIT-7 Ref. 241DON UTD-1F Ref. 242EUO EU-1 Ref. 219,243FAU dealuminated faujasite Ref. 244,245FER siliceous ferrierite Ref. 108,246,247GON GUS-1 Ref. 248IFR ITQ-4 Ref. 109IMF IM-5 Ref. 249ISV ITQ-7 Ref. 250ITH ITQ-13 Ref. 251IWR silica-ITQ-24 Ref. 252MEL silicalite-2 Ref. 253MFI silicalite-1 Ref. 41,203MRE ZSM-48 Ref. 216,254MSE YNU-2 Ref. 255MTT ZSM-23 Ref. 207,256MTW ZSM-12 Ref. 257,258MWW ITQ-1 Ref. 112OKO COK-14 Ref. 259RRO RUB-41 Ref. 197SFE SSZ-48 Ref. 260SFF SSZ-44 Ref. 261SFV SSZ-57 Ref. 262STF SSZ-35 Ref. 261STO SSZ-31 Ref. 263STW HPM-1 Ref. 264TON ZSM-22 Ref. 265,266

polarity and better stability compared to their aluminosilicate analogues, the quality of

the material in terms of its hydrophobicity is also impacted by the relative abundance

of silanol (Si-O-H) defects in the structure. Some of the materials mentioned here have


also been reported to be synthesized in their defect-free forms by using techniques such

as low-pH fluoride synthesis or calcination to heal the silanol defects.

7.3 Low-Polarity Zeolite Synthesis Targets

As discussed in Chapters 4 and 6, this work employs molecular modeling for a large-

scale computational screening of the various all-silica zeolites (and zeotypes) reported

in the IZA–SC database. It should be noted however, that not all of these materials

in the database have been synthesized experimentally in their all-silica forms. So the

next challenge would be to synthesize some of the promising zeolites in their low-polarity

forms and test their performance for the proposed separations. In this sections, synthesis

of two of the most promising framework types, DFT and AWO, and potential future

directions in this regard, are discussed.

7.3.1 Framework Type DFT

Predictions using molecular simulations show that the framework type DFT has a very

high adsorption selectivity (S ≈ 40) towards ethylene over ethane. However, experi-

mentally, this material has never been synthesized as a low polarity all-silica material.

All the attempts in the literature to synthesize this material with different chemical

compositions and the limitations of these materials are summarized here.

Chen et al. first discovered the DFT topology using an organic amine, ethylene-

diamine (NH2-CH2-CH2-NH2), as the SDA for the synthesis. This material (DAF-2)

was a cobalt phosphate with cobalt exclusively in the tetrahedral sites and with a Co/P

ratio of unity. [267] The framework consisted of strictly alternating tetrahedra of Co and

P, leading to negatively charged inorganic framework units of [CoPO4]– , similar to

Lowenstein-limited zeolites with Al/Si ratio of unity. Attempts to remove the charge-

balancing organic template resulted in framework collapse.

Stucky and coworkers synthesized compounds very similar to DAF-2, but with dif-

ferent chemical compositions: UCSB-3 ([ZnAsO4]– ), UCSB-3GaGe ([GaGeO4]– ), and

ACP-3 ([AlxCo1−xPO4]−(1−x), x ≈ 0.15). [268,269] UCSB-3GaGe saw the formation of two

other phases in the reaction mixture and ACP-3 saw impurities of the mineral zeolite

merlinoite. In addition to ethylenediamine, ACP-3 required addition of other organics


such as quinuclidine and piperazine.

Kongshaug et al. synthesized UiO-20, another structure with the DFT topology, but

with a magnesium phosphate chemistry ([Mg4(PO4)4]4−). [270] The 31P NMR indicated

four crystallographically distinct P positions, and therefore the structure exhibited a

supercell (monoclinic; a = 20.9098 Å, b = 17.8855 Å, c = 14.7913 Å, and γ = 134.842◦).

The unit cell of UiO-20 is very different compared to the DAF-2 structure of Chen et

al. (monoclinic; a = 14.719(6) Å, b = 14.734(5) Å, c = 17.891(6) Å, γ = 90.02(2)◦). It

may be worthwhile to note here that the crystallographic data such as space group and

cell constants need not have to be same for the different isotypes and the framework

type (DFT in this case) only refers to the connectivity. Another group synthesized DFT

framework with mixed cobalt and zinc composition: [Zn2−xCox(PO4)2]– (x = 0.61). [271]

Thermogravimetric analysis showed removal of the organic ethylenediamine between

T = 400 − 500◦C, however, the structure collapsed on template removal. Zhao et al.

reported iron zincophosphates with DFT topology, but again, the framework collapsed on

template removal between T = 370− 450◦C. [272] Several other metal phosphate [273–277]

and arsenate [278] forms of DFT framework have also been reported.

Kongshaug et al. have remarked that “DFT has already been found as a germanate,

but it may be difficult to synthesize it as a silicate as the bhs (bifurcated hexagonal

square) chain is rarely observed in silicate compounds”. [270] Barrett et al. have shown

that the DFT topology can be obtained in the aluminosilicate chemistry (with or with-

out incorporation of boron) using ethylenediamine as the SDA and in the presence of

additives such as hydrofluoric acid or boric acid. [279] However, the structure collapsed

above T = 275◦C. Using inorganic cations such as K+ (of KOH) could improve the

stability of the framework to only about T = 325◦C since replacing the organic cation

with the inorganic cation was not quantitatively effective (3–4 K+ per 32 T atoms).

Some of the very promising advantages of this synthesis recipe are: 1:1 ratio of SDA/Si

in the starting gel, relatively lower acid additives (HF or H3BO3) compared to other

studies in the literature. Dong et al. also synthesized the aluminosilicate form of DFT

structure (AS-1) using HF media and ethylenediamine as the SDA. [280] However, these

authors find that the starting composition needs to contain higher SDA/Si and HF/Si

ratios than that of Barrett et al. This could be because of the lower temperature of

100◦C in this study, compared to 150◦C in case of Barrett et al. Under atmospheric


calcination conditions at T = 350◦C, the framework showed no crystallinity and the

SDA was removed at a much higher temperature of about 400◦C.

Ren et al. synthesized an aluminosilicogermanate with a DFT topology (SU-57) by

ethanol-assisted hydrothermal synthesis at T = 160− 170◦C. [281] The crystals had vari-

able Al–Si–Ge composition with [AlSixGe1−xO4]– (x = 0.3− 0.9). The authors showed

that the structure is stable under the N2 atmosphere up to 375◦C, and approximately

2/3 of the organic SDA decomposes at slightly lower temperatures (T = 300− 350◦C).

This suggests that using N2 atmosphere over air for SDA removal may help to improve

framework stability. In this recipe, the starting gel used 31 moles of SDA for every

mole of Al. Additionally, the authors mention that 2/3 of carbon from the template was

eliminated, but all nitrogen of the ethylenediamine SDA was retained. So it is not fully

clear if the framework has been opened up sufficiently for adsorption applications.

Synthesis of an all-silica chemistry with DFT topology using boric acid as a min-

eralizer can be investigated (T ≈ 150◦C and 5–6 days of hydrothermal synthesis using

ethylenediamine). It is possible though that this may lead to a borosilicate, but if the

proportion of boron can be significantly lower, it can be a useful route that avoids the

use of HF. It might also be worth investigating an aluminophosphate synthesis. Since

AlPO materials are neutral, SDA removal may be achievable without framework col-

lapse. Here, phosphoric acid can play a dual role of a phosphorous source and that of

lowering the pH as is done by using HF or boric acid. Such an AlPO synthesis, but

with a different SDA (diethylamine instead of ethylenediamine) has resulted in a struc-

ture that is very similar to DFT, but a different framework type. [282] This shows some

promise for synthesis of DFT in AlPO form using ethylenediamine as the SDA.

7.3.2 Framework Type AWO

Framework type AWO has shown a strong potential for selective removal of H2S not

just from CH4, but also from complex multi-component natural gas mixtures containing

CO2, N2, H2O, ethane, and propane. The synthesis of this framework type and the

difficulty involved in removing the SDA from the synthesized material is discussed here.

Framework type AWO, first discovered in 1985, [283,284] is an eight-membered ring

small-pore unidimensional zeotype with an aluminophosphate chemistry. The AlPO-25

structure consists of tetrahedral phosphorus (PO4) and both tetrahedral (AlO4) and


trigonal-bipyramidal (AlO5) aluminum. Two aluminum pentahedra units are linked

through an OH group and these bridging oxygen atoms hydrogen bond with the proto-

nated amine molecules that are used as SDAs in the synthesis. [199,285] Several different

organic amines such as ethylamine, dimethylamine, n-propyl amine, ethylenediamine,

pyrrolidine, and ethanolamine have been used to synthesize AlPO-21. [283–291] Upon cal-

cination to remove the occluded protonated templates, the structure is unstable and

undergoes dehydration to transform into AlPO4-25, a neural aluminophosphate (Al/P

= 1) with the framework type ATV. [287–289,292]

Synthesis of an all-silica form of the framework type AWO has not been explored in

the literature. Considering that the structure of AlPO-21 comprises of five coordinated

lattice sites, it is difficult to imagine an all-silica synthesis for this material. Note that

the all-silica form of the AWO structure that is reported in the IZA–SC database does

not contain these non-tetrahedral sites and also the three- and five-membered rings in

the original AlPO-21 structure.

Chapter 8

Conclusions

The transferable potentials for phase equilibria (TraPPE) molecular mechanics force

field is extended to hydrogen sulfide. This model comprises of four interactions sites:

Lennard-Jones sites are placed at each of the atomic positions and partial charges are

placed on the hydrogen atoms and a fictitious X site located along the H-S-H bisector.

This representation allows to efficiently and accurately capture the dispersive and elec-

trostatic interactions of H2S for a wide range of physiochemical properties such as pure

and mixture vapor–liquid equilibria, solid–vapor equilibria, critical point, triple point,

temperature dependence of vapor pressure, relative permittivity of liquid and solid H2S,

liquid-phase structure, and the gas-phase self-diffusion coefficient. No special binary

interaction parameters were introduced and only standard Lorentz-Berthelot combining

rules were used to compute the unlike interactions.

One of the main hypotheses of this thesis was that the hydrophobicity of all-silica ze-

olites may be exploited for the selective removal of H2S from moist natural gas streams.

Using the newly developed TraPPE force field for H2S, adsorption of H2S and CH4 in

some select all-silica zeolites was investigated using Gibbs ensemble Monte Carlo simula-

tions. Due to the transferable nature of the TraPPE force field, quantitative agreement

was observed between the fully predictive adsorption isotherm from molecular simula-

tion and the experimental measurements available in the literature. It was found that

in general, an all-silica zeolite has a higher affinity towards H2S compared to CH4 due

to the stronger dispersive interactions or higher condensibility of the former. However,

structure of the all-silica zeolite contributed significantly to the strengths of the favorable

124

Chapter 8: Conclusions 125

binding sites, which in turn impacts the selectivity that each of these zeolites can offer

for the H2S/CH4 separation. Ideal adsorbed solution theory was found to be reasonably

accurate for the H2S/CH4/all-silica zeolite system, but it lacks the quantitative accuracy

to distinguish between various top-performing zeolites. Using binary H2S/H2O adsorp-

tion on silicalite, it was demonstrated that indeed these materials show a selectivity of

about 20 towards H2S versus H2O and supported the hypothesis for the applicability of

all-silica zeolites for bulk H2S removal from ultra-sour natural gas reservoirs.

With this preliminary success for the selective removal of H2S from natural gas, the

computational screening of materials was extended to all the 385 charge-neutral all-silica

zeolite structures that are available in the IZA–SC database. Zeolitic sorbents that can

allow selective removal of H2S from both CH4 and C2H6 were identified using binary

H2S/CH4 and H2S/C2H6 adsorption over a wide range of gas-phase H2S compositions.

A new metric, Q ∗ ln(S), where Q and S are loading and selectivity, respectively, for the

more selective-component, was introduced to rank the different materials being screened.

This metric is based on the stage-based arguments presented earlier and removes the

undue weightage on selectivity when Q ∗ S criteria is used to rank the different mate-

rials. For the first time, the criteria of equal ratios of the mass of the feed mixture to

the mass of the adsorbent was introduced in screening the different materials. This cri-

teria becomes even more important when screening materials for mixtures with three or

more components. For certain promising candidate zeolites, multi-component mixture

simulations were performed and it was observed that the materials retained high selec-

tivity towards H2S even in the presence of other impurities. Also, good correlation was

observed between the selectivities obtained from binary and multi-component mixture

data, suggesting that the materials screening strategy adopted in this study is sufficient

for the sour gas system. This computational study has shown promise for sour natural

gas sweeting with hydrophobic zeolites and opens avenues for experimental studies and

process optimization.

An improved version of the united-atom Trappe force field, TraPPE–UA2, is devel-

oped for ethane and ethylene. The goal was to significantly improve the accuracy of

the models, without compromising much on the efficiency of the TraPPE–UA models.

Ethane is described by a two-site model with the distance between the sites being treated

as a parameter in the force field fitting. The new force field accurately reproduces the

Chapter 8: Conclusions 126

temperature dependence of the saturation vapor pressure, along with other properties

such as critical point and liquid densities. The ethylene model comprises of four sites,

including two LJ interaction sites with a partial positive charge and two compensating

negative partial charges, mimicking the π-bonded electrons in ethylene, placed above

and below the line joining the LJ centers. For the ethylene model, in addition to the

unary VLE, binary VLE with ethane, CO2, and H2O are also included in determining

the choice of parameters. The combining rule has a significant effect on the binary phase

equilibria for molecules with very different LJ diameters, but not for the ethane/ethylene

mixture. The Kong rules are found to perform the best among the three combining rules

assessed in this work and future development, of the TraPPE force field, will consider

this aspect. It is important to note here that the models within TraPPE–small will per-

form better using the Lorentz–Berthelot rule, but interactions of these molecules with

TraPPE–UA2 is described better by the Kong rules. The new ethylene model, that

efficiently and explicitly accounts for the complex quadrupolar interactions and effec-

tive many-body polarization with diverse molecules, opens up the possibility to improve

predictions for ethylene in polar environments, such as cationic zeolites, metal–organic

frameworks, and ionic liquids.

Using these more reliable sets of molecular models for ethane and ethylene, a com-

putational screening of the IZA database of zeolitic structures was performed. It was

shown that for such highly similar molecules, the adsorption and separation predictions

from computational techniques can be highly sensitive to the molecular models that

are employed for the simulations. DFT, ACO, AWO, UEI, APD, and SBN framework

types are predicted to be selective towards ethylene and computation of diffusion en-

ergy barriers for some of these frameworks show that transport may play a significant

role in affecting the breakthrough performance of these materials. Nonetheless, all-silica

synthesis of these framework has not yet been reported and future experimental inves-

tigations on these framework types will help further research in this area. Similarly,

all-silica NAT and JRY frameworks will be interesting synthesis targets for developing

ethane-selective materials.

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Sour Gas Sweetening and Ethane/Ethylene Separation

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