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 Simulation Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.1 Molecular Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.2 Simulation Details . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
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 Simulation Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2.1 Molecular Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2.2 Simulation Details . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2.3 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
vi
5 Transferable Potentials for Phase Equilibria. Improved United-Atom
Description of Ethane and Ethylene 74
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.2 Simulation Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
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
6.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
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)
Chapter 1: Introduction 3
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.
Chapter 1: Introduction 4
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
Chapter 1: Introduction 5
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
Chapter 1: Introduction 6
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
Chapter 1: Introduction 7
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
Chapter 1: Introduction 8
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
Chapter 1: Introduction 9
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
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 12
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 13
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 14
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]
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 15
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 16
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 17
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 18
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.
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 19
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 20
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.
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 21
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 22
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 23
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]
Subscripts denote the standard error of the mean for the last digit(s).Superscripts denote the sources for the experimental data.
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.
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 24
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.
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 25
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 26
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.
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 27
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 28
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 29
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.
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 30
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.
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 31
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 32
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]
Subscripts denote the standard error of the mean for the last digit(s).Superscripts denote the sources for the experimental data.
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.
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 33
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 34
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 35
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 36
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 37
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
Chapter 2: Development of the Transferable Potentials for Phase Equilibria Model forHydrogen Sulfide 38
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
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.
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 41
3.2 Simulation Methodology
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
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 42
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,
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 43
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.
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 44
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 Results and Discussion
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
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 45
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
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 46
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
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 47
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
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 48
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
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 49
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.
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 50
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
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 51
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.
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 52
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
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 53
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
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 54
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
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 55
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,
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 56
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
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 57
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
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 58
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%
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 59
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.
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 60
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
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 61
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
Chapter 3: Monte Carlo Simulations Probing the Adsorptive Separation of HydrogenSulfide/Methane Mixtures Using All-Silica Zeolites 62
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
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.
201600612&attachmentId=149228245
Chapter 4: Identifying Optimal Zeolitic Sorbents for Sweetening of Highly Sour NaturalGas 65
between the data at different state points (see SI).
4.2 Simulation Methodology
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
Chapter 4: Identifying Optimal Zeolitic Sorbents for Sweetening of Highly Sour NaturalGas 66
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
Chapter 4: Identifying Optimal Zeolitic Sorbents for Sweetening of Highly Sour NaturalGas 67
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,
Chapter 4: Identifying Optimal Zeolitic Sorbents for Sweetening of Highly Sour NaturalGas 68
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.
4.3 Results and Discussion
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
Chapter 4: Identifying Optimal Zeolitic Sorbents for Sweetening of Highly Sour NaturalGas 69
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
Chapter 4: Identifying Optimal Zeolitic Sorbents for Sweetening of Highly Sour NaturalGas 70
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
Chapter 4: Identifying Optimal Zeolitic Sorbents for Sweetening of Highly Sour NaturalGas 71
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
Chapter 4: Identifying Optimal Zeolitic Sorbents for Sweetening of Highly Sour NaturalGas 72
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)
Chapter 4: Identifying Optimal Zeolitic Sorbents for Sweetening of Highly Sour NaturalGas 73
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
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.
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 76
5.2 Simulation Methodology
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
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 77
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
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 78
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.
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 79
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.
5.3 Results and Discussion
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
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 80
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&
attachmentId=198526525
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 81
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,
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 82
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
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 83
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.
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 84
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
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 85
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
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 86
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
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 87
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%
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 88
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
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 89
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
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 90
(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.
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 91
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.
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 92
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
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 93
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
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 94
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
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 95
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
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 96
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
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 97
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
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 98
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.
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 99
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
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 100
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.
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 101
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.
Chapter 5: Transferable Potentials for Phase Equilibria. Improved United-AtomDescription of Ethane and Ethylene 102
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
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
Chapter 6: C2 Adsorption in Zeolites: In Silico Screening and Sensitivity to MolecularModels 105
(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
Chapter 6: C2 Adsorption in Zeolites: In Silico Screening and Sensitivity to MolecularModels 106
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.
6.3 Results and Discussion
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
Chapter 6: C2 Adsorption in Zeolites: In Silico Screening and Sensitivity to MolecularModels 107
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
Chapter 6: C2 Adsorption in Zeolites: In Silico Screening and Sensitivity to MolecularModels 108
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
Chapter 6: C2 Adsorption in Zeolites: In Silico Screening and Sensitivity to MolecularModels 109
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
Chapter 6: C2 Adsorption in Zeolites: In Silico Screening and Sensitivity to MolecularModels 110
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
Chapter 6: C2 Adsorption in Zeolites: In Silico Screening and Sensitivity to MolecularModels 111
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).
Chapter 6: C2 Adsorption in Zeolites: In Silico Screening and Sensitivity to MolecularModels 112
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.
Chapter 6: C2 Adsorption in Zeolites: In Silico Screening and Sensitivity to MolecularModels 113
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.
Figure 6.5 shows the pure-component adsorption isotherms of ethane and ethylene
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
Chapter 6: C2 Adsorption in Zeolites: In Silico Screening and Sensitivity to MolecularModels 114
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.
Figure 6.6 shows the pure-component adsorption isotherms of ethane and ethylene
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
Chapter 6: C2 Adsorption in Zeolites: In Silico Screening and Sensitivity to MolecularModels 115
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
Chapter 7: Zeolite Synthesis: Literature Survey and Potential Future Targets 118
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
Chapter 7: Zeolite Synthesis: Literature Survey and Potential Future Targets 119
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
Chapter 7: Zeolite Synthesis: Literature Survey and Potential Future Targets 120
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
Chapter 7: Zeolite Synthesis: Literature Survey and Potential Future Targets 121
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
Chapter 7: Zeolite Synthesis: Literature Survey and Potential Future Targets 122
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
Chapter 7: Zeolite Synthesis: Literature Survey and Potential Future Targets 123
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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