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DESIGN METHOD FOR LAYERED BED ADSORBER FOR SEPARATION OF
CO2 AND N2 FROM NATURAL GAS USING ZEOLITE13X, CARBON
MOLECULAR SIEVE AND ACTIVATED CARBON
A Thesis
Submitted to the Faculty of Graduate Studies and Research
In Partial Fulfillment of the Requirements for the
Degree of Master of Applied Science
in
Process Systems Engineering
University of Regina
By
Mohammad Rokanuzzaman
Regina, Saskatchewan
February, 2015
Copyright 2015: Mohammad Rokanuzzaman
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UNIVERSITY OF REGINA
FACULTY OF GRADUATE STUDIES AND RESEARCH
SUPERVISORY AND EXAMINING COMMITTEE
Mohammad Rokanuzzaman, candidate for the degree of Master of Applied Science in Process Systems Engineering, has presented a thesis titled, Design Method for Layered Bed Adsorber for Separation of CO2 and N2 from Natural Gas Using ZEOLITE13X, Carbon Molecular Sieve and Activated Carbon, in an oral examination held on December 16, 2014. The following committee members have found the thesis acceptable in form and content, and that the candidate demonstrated satisfactory knowledge of the subject material. External Examiner: Dr. Daoyong Yang, Petroleum Systems Engineering
Supervisor: Dr. Amornvadee Veawab, Process Systems Engineering
Committee Member: Dr. Stephanie Young, Process Systems Engineering
Committee Member: Dr. Adisorn Aroonwilas , Industrial Systems Engineering
Chair of Defense: Dr. Doug Durst, Faculty of Social Work
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ABSTRACT
Natural gas (NG) is a low-carbon fossil fuel that carries impurities such as carbon
dioxide (CO2) and nitrogen (N2). These two impurities reduce the heating value of NG.
Also, CO2 causes corrosion in the pipeline and N2 produces nitrogen oxide (NOx) when
combusted. These facts have forced NG transmission and distribution companies to limit
the concentrations (mole percent) of CO2 (≤ 3%) and N2 (≤4%). Consequently, selective
separation of CO2 and N2 from NG has gained considerable importance.
There are many technologies that are in use for separation of these two
constituents. Most of them are suitable for single component separation: either CO2 or
N2. In the context of multicomponent separation common in industries, adsorption is an
emerging technology that offers low-cost and energy-efficient separation for small- to
medium-sized industries. The technology lacks commercial availability due to its
dependency of design methodologies on experimentation, simulation or both.
This work focuses on easy-to-use design methodology for the design of a double
bed adsorber. This easy-to-use methodology is tailored for separation of CO2 and N2 from
NG using zeolite13X and a carbon molecular sieve (CMS3K) or activated carbon (ACB).
These adsorbents are commercially available, and they offer easy and energy efficient
regeneration for repeated uses. The product will meet the specified concentration limit for
NG transmission and distribution systems.
To achieve this goal, two layered bed adsorbers, zeolite13X-CMS3K and
zeolite13X-ACB, were simulated using Aspen Adsorption. Simulation requires a
trustworthy mathematical framework i.e. model. Therefore, a model was developed in
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Aspen adsorption by selecting relevant equations and submodels. Inputs for the model
were collected from literature, calculated using various equations, and obtained by fitting
experimental data. A numerical solution method was specified and, finally, the model
was validated against experimental measurements.
A parametric study was performed for a wide range of operating conditions. Data
generated through parametric study were correlated. The correlations, the first of this
kind, can be used to predict required amounts of adsorbents for 100% CO2 separation and
50 to 90% N2 separation. Finally, a procedure was outlined to transform the amount of
adsorbent into the physical dimensions of an adsorber.
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ACKNOWLEDGEMENTS
I would like to express my sincere gratitude to my supervisor, Dr. Amornvadee
Veawab, for giving me the opportunity to carry out this interesting research under her
enthusiastic supervision. Her enormous financial and technical support, valuable
guidance, and encouragement were a great source of inspiration and the driving force
throughout the entire course of this research. I would also like to express my gratitude to
Dr. Adisorn Aroonwilas for his great support, guidance, and encouragement.
I would like to thank the Natural Sciences and Engineering Research Council of
Canada (NSERC), SaskEnergy, and the Faculty of Graduate Studies and Research
(FGSR) for their financial support. I would also like to thank the Faculty of Engineering
and Applied Science at the University of Regina for their help and support.
Finally, I am sincerely thankful and grateful to my parents, family, and friends
for their unconditional love, prayers, and support to fulfill my dreams.
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Table of contents
Abstract i
Acknowledgement iii
Table of contents iv
List of Tables vii
List of Figures ix
Nomenclature xii
1. Introduction 1
1.1 Natural gas 1
1.2 Industrial separation processes for removal of N2 and CO2 from natural gas 3
1.3 Adsorption process and adsorbents for CO2 and N2 removal 5
1.4 Modeling and simulation 7
1.5 Research motivation, objectives and scope of work 9
2. Literature review 12
2.1 Scope of review 12
2.2 Adsorption fundamentals 12
2.3 Adsorbents 13
2.3.1 Zeolite13X 14
2.3.2 Carbon adsorbents 15
2.4 Adsorption modeling 17
2.5 Multicomponent separation 20
2.6 Numerical Solution of partial differential equations 22
3. Modeling and simulations of a gas adsorber 25
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3.1 Adsorption modeling 25
3.1.1 Model equations 27
3.1.2 Solution of model equations 34
3.1.3 Calculation procedure 35
3.2 Model validation 38
3.2.1 Nitrogen separation using activated carbon 38
3.2.2 Methane separation from hydrogen using Zeolite 5A 42
3.2.3 Carbon dioxide separation using Zeolite 13X 45
4. Results and Discussion 50
4.1 Description of simulated gas adsorption systems 50
4.2 Simulation results for zeolite13X 52
4.2.1 Parametric study 56
4.2.2 Correlation to determine amount of zeolite13X 61
4.3 Simulation results for zeolite13X-CMS3K system 64
4.3.1 Parametric Study 68
4.3.2 Correlations based on simulated results 73
4.4 Simulation results for zeolite13X-ACB system 77
4.4.1 Parametric study 81
4.4.2 Correlations based on simulated results 86
4.5 Determination of column dimensions using correlations 89
5. Conclusions and recommendation for future work 92
5.1 Conclusions 92
5.2 Recommendation for future work 94
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References 95
Appendix – A: Adjustments of transport parameters 106
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List of Tables
Table 1.1 Quantity of air pollutants produced from fossil fuel combustion in
lbs/billion Btu (U.S. Energy Information Administration (EIA),
1999)
2
Table 1.2 Composition of natural gas observed in different reservoirs as
mole percentage (Kidnay and Parish, 2006)
2
Table 1.3 Specification of pipeline natural gas (modified from Kidnay and
Parish, 2006)
4
Table 3.1 Model equations 26
Table 3.2 Model input (N2-ACB system) 40
Table 3.3 Model inputs (CH4-H2-zeolite5A system) 43
Table 3.4 Model inputs (CH4-CO2-N2-zeolite13X system) 46
Table 3.5 Isotherm parameters (CH4-CO2-N2-zeolite13X system) 47
Table 4.1 Physical properties of zeolite13X and properties of column
(Cavenati et al., 2006)
53
Table 4.2 Parameters used in simulation for zeolite13X 54
Table 4.3 Parameters of correlation for determination of amounts of
zeolite13X
62
Table 4.4 Physical properties of double bed adsorber (zeolite13X-CMS3K)
(Cavenati et al., 2006)
65
Table 4.5 Parameters used in simulation of zeolite13X-CMS3K system 66
Table 4.6 Parameters for correlations 4.2 75
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Table 4.7 Physical properties of double bed adsorber (zeolite13X-ACB)
(Cavenati et al., 2006 and Shen et al., 2010)
78
Table 4.8 Parameters used in simulation of zeolite13X-ACB system 79
Table 4.9 Parameters for correlation 4.3 87
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List of Figures
Figure 3.1 Calculation procedure 37
Figure 3.2 Breakthrough concentration profiles of N2 in pitch-based AC
beads (0.5% N2 in helium at 303K and 1 bar) under isothermal
conditions
41
Figure 3.3 Breakthrough concentration profile of methane in Zeolite 5A
(8.8% Methane in Hydrogen at 303K and 20.2 bar) under
isothermal conditions
44
Figure 3.4 Breakthrough concentration profiles of 70% CH4, 20% CO2 and
10% N2 in Zeolite 13X at 300K and 2.5 bars
48
Figure 3.5 Temperature profile at bed exit (70% CH4, 20% CO2 and 10%
N2 in Zeolite 13X at 300K and 2.5 bars)
49
Figure 4.1 Double bed adsorber 51
Figure 4.2 Required amount of zeolite13X for complete separation of CO2
as a function of feed pressure
55
Figure 4.3 Adsorption capacities and selectivity for CO2-N2-zeolite13X
system
57
Figure 4.4 Effect of concentration (%) of CO2 on required amount of
zeolite13X for 100% separation of CO2
59
Figure 4.5 N2 separation efficiency of zeolite13X 60
Figure 4.6 Comparison of simulated and predicted amounts of zeolite13X 63
Figure 4.7 Total amount (kg/mol of feed gas) of adsorbents for N2 and CO2 67
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separation from natural gas for zeolite13X-CMS3K adsorber
Figure 4.8 Effect of feed pressure on N2 separation efficiency (%) for
zeolite13X-CMS3K system
68
Figure 4.9 Effect of feed gas pressure on total amount of adsorbents for 70
to 90% N2 separation efficiency for zeolite13X-CMS3K system
70
Figure 4.10 Effect of feed concentration on nitrogen separation efficiency at
2.5 bars for zeolite13X-CMS3K system
72
Figure 4.11 Effect of N2 separation efficiency on total amount of adsorbent
for zeolite13X-CMS3K system
74
Figure 4.12 Comparison of simulated result with the results obtained from
correlation 4.2 for feed composition of 75% CH4, 15% N2 and
10 % CO2 for zeolite13X-CMS3K system
76
Figure 4.13 Total amount of adsorbents for N2 separation at different feed
pressures and compositions (zeolite13X-ACB system)
80
Figure 4.14 Effect of feed pressure on total amount of adsorbent for different
N2 separation efficiency (zeolite13X-ACB system)
82
Figure 4.15 Effect of concentration on total amount of adsorbents at different
feed pressures for zeolite13X-ACB system
84
Figure 4.16 Effect of N2 separation efficiency on total amount of adsorbent
for feed pressures of (a) 2.5 bars and (b) 30 bars (zeolite13X-
ACB system)
85
Figure 4.17 Comparison of simulated and predicted (correlation 4.3) results 88
Figure 4.18 Calculation procedure for determination of column dimension 91
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using correlations
Figure A.1 Breakthrough of CO2 in zeolite13X for various mass transfer
resistances
107
Figure A.2 Breakthrough of CO2 in zeolite13X with modified macropore
resistance
109
Figure A.3 Effect of conductivity (gas and solid) on breakthrough dynamics 111
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Nomenclature
C0 Initial concentration (kmol/m3)
Ci Molar concentration (kmol/m3)
Cpa Specific heat capacity of adsorbed phase (MJ/kmol/K)
Cps Specific heat capacity of adsorbent (MJ/kmol/K)
Cpw Specific heat capacity of column wall (MJ/kg/K)
Cvg Specific gas phase heat capacity at constant volume (MJ/kmol/K)
Da Axial dispersion coefficient (m2/s)
DAB Binary diffusivity (cm2/sec)
Db Bed diameter (m)
Dk Knudsen diffusivity
Dm Molecular diffusivity
Dp Pore diffusivity (m2/s)
Hamb Wall-ambient heat transfer coefficient (MW/m2/K)
Hw Gas-wall heat transfer coefficient (MW/m2/K)
K Dimensionless Henry’s constant
KH Henry’s constant
M Molecular weight (kg/kmol)
Nu Nusselt number
P Feed pressure (bar)
PeH Peclet number for gas wall heat transfer
Pr Prandtl number
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Q Amount of adsorbents (g or kg per mol of feed gas)
Rc Crystal radius (m)
Re Reynolds Number
S Separation factor (mol/mol)
Sc Schmidt Number
Sh Sherwood Number
T0 Wall temperature (K)
Tamb Ambient temperature (K)
Tg Gas phase temperature (K)
Ts Solid phase temperature (K)
Tw Wall temperature (K)
V Atomic diffusion volume
WT Width of column (m),
Z Height of adsorbent bed (m)
ap Specific particle surface per unit volume bed (m2 (Particle area)/m
3 (Bed))
dp particle diameter (m)
hf Gas-solid heat transfer coefficient (MW/m2/K)
k Effective mass transfer coefficient
kf Film mass transfer coefficient (m/s),
kg Conductivity of gas phase
q0 Initial loading (kmol/kg)
q Loading (kmol/kg)
q* Instantaneous equilibrium concentration (kmol/kg)
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rmac Macropore radius
rp Particle radius (m)
t Time (second)
w Solid phase concentration (kmol/kg)
yi Mole fraction of component i
εb Bed voidage
εi Interparticle voidage
νg Gas velocity (m/s)
μ Dynamic viscosity (N s/m2)
η Separation efficiency (%)
μmix Viscosity of gas mixture
ψ Shape factor
ρg Gas phase molar density (kmol/m3)
ρmix Density of gas mixture
ρs Adsorbent bulk density (kg/m3)
ρw Wall density (kg/m3)
φij Binary viscosity of gas mixture
τ Tortuosity
ΔHi Heat of adsorption (MJ/kmol).
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1 Introduction
1.1 Natural gas
More than 80% of energy comes from carbon-based fossil fuel (coal, oil, and
natural gas), and such contribution is expected to remain the same until 2030 (World
Energy Council, 2010). Combustion of these fossil fuels produces carbon dioxide (CO2),
which has already raised concern regarding global warming and climate change. Some
other pollutants that are also associated with fossil fuel combustion are carbon monoxide
(CO), nitrogen oxides (NOx), sulfur dioxide (SO2), particulate matters (PMs),
formaldehyde (CH2O), and mercury (Hg) (Table 1.1). These pollutants pose adverse
impacts on human health and the environment. Among the fossil fuels, natural gas is
considered to be the cleanest fossil fuel as it produces fewer quantities of CO2, NOx, SO2,
PMs, and Hg than coal and oil (EIA, 1999).
Natural gas is a complex mixture of hydrocarbons (such as methane, ethane,
propane, butane, and heavier hydrocarbons) and nonhydrocarbons (such as N2, CO2, and
hydrogen sulfide (H2S)). It may be present as free gas (bubbles) or dissolved in either
crude oil or brine under reservoir conditions in hundreds of different components with
various concentrations. Even two wells in the same reservoir may yield different natural
gas compositions (Younger, 2004). For example, as shown in Table 1.2, the
concentrations of CH4 vary from 29.98 to 96.91%, while the concentrations of N2 and
CO2 vary from 0.68 to 26.1% and 0.82 to 42.66%, respectively. Some reservoirs other
than those shown in Table 1.2 may have extreme contents of CO2 (92%), N2 (86%), and
H2S (88%) (Hobson and Tiratso, 1985).
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Table 1.1: Quantity of air pollutants produced from fossil fuel combustion in lbs/billion
Btu (U.S. Energy Information Administration (EIA), 1999)
Pollutant Natural Gas Oil Coal
Carbon dioxide 117000 164000 208000
Carbon monoxide 40 33 208
Nitrogen oxide 92 448 457
Sulfur dioxide 0.60 1122 2591
Particulates 7 84 2744
Formaldehyde 0.75 0.22 0.221
Mercury 0.0005 0.007 0.016
Table 1.2: Composition of natural gas observed in different reservoirs as mole percentage
(Kidnay and Parish, 2006)
Component Canada
(Alberta)
Western
Colorado
Southwest
Kansas
Bach
Ho
Vietnam
Miskar
Tunisia
Cliffside
Texas
Rio
Arriba
New
Mexico
Methane 77.1 29.98 72.89 70.85 63.90 65.80 96.91
Ethane 6.60 0.55 6.27 13.41 3.35 3.80 1.33
Propane 3.10 0.28 3.74 7.50 0.96 1.70 0.19
Butane 2.00 0.21 1.38 4.20 0.54 0.80 0.05
Pentane and
heavier
3.00 0.25 0.62 2.64 0.63 0.50 0.02
Helium 0 0 0.45 0 0 1.8 0
Nitrogen 3.20 26.10 14.65 0.21 16.90 25.60 0.68
Carbon dioxide 1.70 42.66 0 0.06 13.58 0 0.82
Hydrogen sulfide 3.30 0 0 0 0.09 0 0
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Natural gas is typically processed to meet pipeline specifications (Table 1.3),
which are intended to deliver the natural gas with high heating value to the end users and
also to protect pipeline from corrosion and plugging. For example, to prevent corrosion,
the concentrations of CO2, H2S, and mercaptans or total sulfur are limited to less than 3%
(mole), 6–7 mg/m3, and 115–460 mg/m
3, respectively, while to prevent liquid dropout,
the concentrations of butane and heavier hydrocarbons are limited to less than 2.0%
(mole) and less than 0.5%, respectively. This study focuses on separation of CO2 and N2
from natural gas for the purpose of compliance to the pipeline gas specification. These
two gases are considered to be the contaminants of natural gas since they have no heating
value and occupy transport volume. The CO2 corrodes pipelines in the presence of water
and the N2 produces NOx when natural gas is combusted.
1.2 Industrial separation processes for removal of N2 and CO2 from natural gas
Four gas separation techniques, namely, cryogenic distillation, membrane
separation, absorption, and adsorption are in practice for natural gas purification. Of
these, the cryogenic and absorption processes are economically viable at high gas
throughputs (> 15 MMscfd), while the membrane and adsorption processes are viable at a
gas throughputs of 0.5 - 25 MMscfd and 2 - 15 MMscfd, respectively (Kidnay and Parish,
2006). The absorption process is widely used for CO2 capture while the cryogenic
process is established for N2 removal from natural gas. Neither of these two processes is
suitable for removal of both CO2 and N2 simultaneously. The cryogenic process for N2
separation requires extensive pretreatments that eliminate CO2 from feed gas.
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Table 1.3: Specification of pipeline natural gas (modified from Kidnay and Parish, 2006)
Components Quantity (mole % or as mentioned)
Methane 75.0% (minimum)
Ethane 10.0% (maximum)
Propane 5.0% (maximum)
Butane 2.0% (maximum)
Pentanes and heavier 0.5% (maximum)
Nitrogen 4.0% (maximum)
Carbon dioxide 3.0% (maximum)
Hydrogen sulfide 6 to 7 mg/m3
Total sulfur 115-460 mg/m3
Water vapor 60-110 mg/m3
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Additionally, these two processes incur high operating costs compared to membrane or
adsorption processes (Robertson, 2007).
Conventional membrane (cellulose acetate/polysulfone) separation technologies
use kinetic diameters of molecules as the separation criterion. The kinetic diameters of
CH4, CO2, and N2 are 3.8Å, 3.3Å, and 3.6Å, respectively (Do, 1998). These diameters are
too close to offer a favorable selectivity for membrane. Silicone membrane separation
uses equilibrium affinity as the separation criterion. In CH4-N2 separation using this
membrane, CH4 comes out at low pressure end and, hence, leads to additional
recompression costs. Another critical element of the process is the pretreatment of the
feed gas since particulates block the membrane openings and liquids cause swelling,
resulting in decreased performance and even physical damage. Membranes can be highly
efficient mass-separating mediums, especially when the species that are to pass through
the membrane are present in a large concentration (Choi et al., 2009).
Adsorptive separation is a process where certain fluid particles are bonded to the
surface of an adsorbent by physical/chemical bonding. It is based on three distinct
mechanisms: steric (dimension: pore and molecule size), equilibrium (accommodation
ability), and kinetic (diffusion rate) mechanisms (Do, 1998). The first step in separation is
adsorption during which species are preferentially picked up from the feed by
adsorbent/adsorbents (porous solid), and the second is regeneration or desorption during
which the species are removed from the adsorbent. There are two types of adsorption
processes: physical adsorption and chemical adsorption. Of them, the physical-adsorption
process is an energy efficient and low cost technology (Siriwardane et al., 2001).
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1.3 Adsorption process and adsorbents for CO2 and N2 removal
The separation efficiency of the adsorption process depends on the quality of the
adsorbent, a porous solid. Ideally, an adsorbent should have large adsorption capacity,
fast adsorption and desorption kinetics, infinite regenerability, and a wide yet tunable
range of operating conditions (Choi et al., 2009). However, in practice, it is rare to find
such an ideal adsorbent. Another adsorption behavior to consider is the competitive
adsorptions, known as selectivity, of components (CO2/N2/CH4) of a gas mixture (natural
gas, considered to be a mixture of CH4, CO2, and N2 for simplicity). Thus, optimizing the
trade-off between beneficial and non-beneficial features is the key in process design and
operation.
The adsorbents that have been used for CO2 separation are zeolites (crystalline
aluminosilicates), activated carbons, calcium oxides, hydrotalcites, and supported amines.
A review of these materials can be found in Choi et al. (2009). The zeolite-based
adsorbents were reported to yield relatively high adsorption capacities (Ding and Alpay,
2000). Harlick and Tezel (2004) carried out an experimental screening study of various
synthetic zeolite adsorbents and reported that zeolite13X possesses a maximum CO2
adsorption capacity of 4.5 mol/kg at 1 bar and 295K. Typically, the zeolites recover fresh
adsorption capacity when regenerated, though little irreversible behavior was reported by
Brandani and Ruthven (2004). Zeolite13X also provides high selectivity for CO2 over
CH4 and N2 (Cavenati et al., 2004).
The adsorption of N2 on several commercial adsorbents was studied by many
researchers. Of these, carbon-based adsorbents, such as the carbon molecular sieve
(CMS) and activated carbon bead (ACB), showed greater adsorption capacity (0.27
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mol/kg at 303K and 100 kPa) (Shen et al., 2010). The notable difference between these
two adsorbents is in pore distribution. ACB carries both micropores and transitional pores
ranging from 10 to 500 Angstroms (Å), while CMS contains uniform pores of less than
10 Å (Do, 1998). The porous structures of ACB and CMS lead to equilibrium-based
separation and kinetic-based separation, respectively. In equilibrium-based separation,
the equilibrium selectivity of these carbonaceous adsorbents favors CH4 over N2, which
eventually renders more adsorbed CH4 at the surface of the adsorbents. In kinetic-based
separation, the kinetic selectivity of N2 over CH4, offered by CMS, leads to less
adsorption of CH4 in adsorbents. An advantage of equilibrium-based separation is that it
offers longer cycle time than its counterpart: kinetic separation. Both ACB and CMS
have greater affinity for CO2 than either CH4 or N2, which leads to the necessary removal
of CO2 from the natural gas to facilitate optimum nitrogen separation. In this study,
zeolite13X was used to separate CO2 from a ternary mixture of CH4, CO2, and N2. ACB
and CMS were used to separate N2 from a binary mixture of CH4 and N2.
1.4 Modeling and simulation
In adsorption separation systems, the process variables are strongly coupled,
resulting in complex interrelationships. Therefore, the effect of any single variable on
separation efficiency is simply unpredictable by simple reasoning or empiricism (Hassan
et al., 1986). Furthermore, a change in adsorbent material adds additional complexity due
to their unique adsorbate-adsorbent behaviour under the same operating conditions
(Flores-Fernandez and Kenney, 1983). Thus, the design and optimization requires either
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extensive experimentation or the guidance of a predictive model (Farooq and Ruthven,
1991).
An adsorption model requires in-depth mechanistic knowledge of the kinetics and
equilibria of adsorption process and their impact on the dynamic response of an
adsorption column (Ruthven, 2000). The pioneer studies of kinetics and equilibria
include, but are not limited to, the works of Habgood (1958), Barrer et al. (1963), and
Mayers and Prausnitz (1965). These studies reveal that the adsorption separation
efficiency is controlled by either equilibrium or kinetics.
The simplest adsorption model uses the equilibrium theory. Thomas (1944) can be
credited to be the pioneer of the use of equilibrium theory in an ion exchange column.
His work was later shaped by Glueckauf (1955) and Rosen (1952) in a general form for
application in gas adsorption processes. Such an equilibrium model accommodates the
analytical solution of the governing material balance equations and provides useful
behavioral insights. However, the theory does not consider real situations such as partial
equilibrium and dispersive flows observed in an industrial setup. This model also ignores
the mass transfer resistances (Hassan et al., 1986). Failure of incorporating such
important process characteristics resulted in outsized deviations in the adsorption of CO2
on silica gel (Mitchell and Shendahnan, 1972) and that of ethylene on zeolite 4A/5A
(Hassan et al., 1985).
The limited success of equilibrium models necessitates consideration of kinetic
models as well. A kinetic model requires adequate representation of mass transfer
kinetics. Mitchell and Shendahnan (1973) adopted this approach with one mass transfer
resistance and constant velocity. They laid the foundation of a dynamic model that, later
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on, comprehensibly described the mass transfer kinetics as well as resistances (Hassan et
al., 1986). This dynamic model accounts for realistic scenarios, such as axial mixing and
mass transfer resistances, which are always likely to be present in the practical systems.
The model is, therefore, more realistic and sufficiently general to be applied for detailed
optimization studies of both systems.
The dynamic model equations then become very complicated and, hence, were
solved numerically. Various numerical solution procedures were facilitated by the use of
computers in the early 1980s. This trend gradually paved the way for the development of
process simulators (Ruthven, 2000). The research performed by Liapis and Crosser
(1982), one of the earliest examples, served as the foundation of commercial simulators
such as Aspen Adsorption (Nilchan and Pantelides, 1998). The availability of such
simulators made it possible to simulate the adsorption process with more rigorous
mathematical models by greatly reducing the burden of the manual handlings of complex
equations and their numerical solutions. The use of such simulators is not limited to
merely solving some equations but rather has expanded into the design and optimization
of commercial processes.
1.5 Research motivation, objectives and scope of work
The separation of CO2 and N2 from NG is a two-step separation process as two
adsorbents, CO2 selective and N2 selective, are required. This can be done in a single
column using layers of different adsorbents (Chlendi et al., 1995; Chlendi and Tondeur,
1995; Malek and Farooq, 1998; Yang and Lee, 1998; Lee et al., 1999; Jee et al., 2001;
Takamura et al., 2001; Cavenati et al., 2006; Rebeiro et al., 2008) or columns in series
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carrying different adsorbents (Sircar, 1979; Kumar, 1990). Of these two types of adsorber
combination, the layered bed adsorber offers compact design and operation flexibility.
Layered bed adsorption systems were studied by many researchers, as mentioned
above, for the separation of various components, such as CO2, N2, CH4, CO, on various
adsorbents. A discussion on the layered bed adsorption system is included in Chapter 2.
Of the studies mentioned, the most relevant study for the separation CO2 and N2 from NG
was published by Cavenati et al. (2006). They studied a layered bed adsorber containing
zeolite13X and CMS3K in terms of product purity and separation efficiency and the
effects of the ratio of bed height on separation efficiency. It was concluded that the bed
ratio has an insignificant effect on product purity and separation efficiency. For their
study, they used a single feed pressure (2.5 bars) and two compositions (mole %) of feed
gas (70% CH4/20% CO2/10% N2 and 60% CH4/20% CO2/20% N2). No conclusions were
drawn for other concentrations or other feed pressures. This study is good for conveying
an understanding of the adsorption behavior of CO2 and N2 in a mixture of CH4-CO2-N2.
No methodology for the design of a double bed adsorber was outlined.
To this end, this study aims to develop an easy-to-use design methodology for a
layered bed adsorber using commercial adsorbents. The method shall cover a wide range
of operating conditions consistent with CO2 and N2 concentrations observed in various
reservoirs and typical feed pressure of NG distribution pipelines. Also, the product shall
meet the concentration limit of CO2 and N2 in an NG distribution network to maintain
pipeline integrity and product purity. The method shall significantly reduce the need for
extensive experiment and simulation.
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To achieve such an objective, a standalone simulation study was performed on a
two-layered bed adsorption system (zeolite13X-CMS3K and zeolite13X-ACB) in Aspen
Adsorption, a commercial simulator (discussed in Chapter 2). Since such study requires a
trustworthy mathematical framework or model, a model was developed using the
resources of the simulator. Required inputs were gathered from the literature, calculated
using various equations/correlations, and obtained through fitting the experimental data.
To justify the reliability of the model, it was validated against several adsorption
processes that covered various operating conditions on different adsorbents.
Parametric studies were performed for a wide range of operating conditions that
covered concentrations observed in various NG reservoirs and feed pressures of typical
NG distribution networks. The data generated through parametric study were correlated.
The correlation, the first of this kind, predicts the amount of adsorbents for 100% CO2
separation and 50-90% N2 separation. A step-by-step procedure was outlined to
transform the amount of adsorbent into physical dimensions of the adsorption column.
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2 Literature Review
2.1 Scope of review
Charles W. Skarstorm was awarded the first patent on a commercial adsorptive
separation process for air fractionation in 1960. Since then, the technology has gained a
phenomenal growth in commercial applications and process concepts (Sircar, 2006). This
chapter addresses process fundamentals and essential components of process design that
has led the technology to the present state.
2.2 Adsorption fundamentals
Adsorption is a surface phenomenon that refers to enrichment (or rise in density)
of material at the vicinity of fluid-solid interfaces through physical or chemical bonding
(Rouquerol et al., 1999). The fluid is referred as an adsorbate and the solid is referred to
(porous and permeable) as adsorbents. An adsorbent selectively adsorbs a component or
components from a mixed feed. Such selective adsorption may depend on the difference
in adsorption at equilibrium or on a difference in adsorption rates.
There are three distinct mechanisms through which adsorption separation takes
place (Yang, 2003). They are (i) steric or molecular sieving effects, (ii) kinetic or
diffusional effects, and (iii) equilibrium or selective adsorption effects. The steric effect
allows small and properly shaped molecules to diffuse into adsorbent where the
molecules are consequently adsorbed while other molecules are barred from entering the
pores. The success depends on the pore diameter of adsorbents and the kinetic diameter
and shape of fluid particles. Examples of steric separation include gas drying with 3A
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13
zeolite and the separation of normal paraffins from iso-paraffins and other hydrocarbons
with 5A zeolite (Yang, 1987). Kinetic separation is achieved by virtue of differences in
diffusion rates and, hence, the mechanism is also known as partial molecular sieving
action. For effective separation, the pore size needed to be precisely controlled between
the kinetic diameters of the molecules to be separated (Yang, 2003). Nitrogen-methane
separation with 5A zeolite and nitrogen-oxygen separation with a carbon molecular sieve
are examples of kinetic separations. An equilibrium effect uses the adsorbate-adsorbent
interaction at the solid surface when all the components of a gas mixture are present. The
strength and affinity of fluid particles determines selective adsorption of components.
Separation of carbon dioxide and methane with zeolite is an example of equilibrium
separation. In a practical process, any of the mechanisms or any combination of these
mechanisms may play a significant role since all of the mechanisms depend on the
geometry and topology of the adsorbent (Rigby et al., 2004).
2.3 Adsorbents
The essential component of an adsorption separation process is the adsorbent. As
for industrial applications, it is a structured solid with inter-connected voids that hold a
certain fluid and, hence, separates a contaminant from the bulk of fluids. Characteristics
of adsorbents have been described by various researchers. A summary can be found
elsewhere (Rigby et al., 2004). The description includes the origin, size, structure, and
inter-connectivity of pores. The portrayal of pores in terms of size, distribution, and inter-
connectivity has found widespread applications in industries. An adsorbent with
interconnected pores of the same distribution is known as a homogeneous adsorbent
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14
(silica gel, activated carbon, activated alumina, etc.). In contrast, heterogeneous (carbon
molecular sieve, zeolite), also known as composite, adsorbent consists of pellets of
microporous crystal that result in a bidispersity in pore networks.
Several features illustrate the quality or usefulness of an adsorbent. In general, an
ideal or hypothetical adsorbent should have large adsorption capacity, fast adsorption and
desorption kinetics, infinite regenerability and stability, and a wide yet tunable range of
operating conditions (Choi et al., 2009). In reality, no single ideal adsorbent is likely to
exist and an effective separation process uses trade-offs of these features. Three
adsorbents (zeolite13X, activated carbon, and a carbon molecular sieve) were considered
in this study. Relevant discussion on these three adsorbents is included in next three
subsections.
2.3.1 Zeolite13X
Zeolites are tridimensional aluminosilicates: a periodic array of SiO4/AlO4
composed of Si and Al tetrahedra linked through bridging oxygen atoms giving rise to a
periodic distribution of pores and cavities of particular molecular dimensions. This
microporous adsorbent represents a major breakthrough in the adsorption separation
process due to their uniform pore structure (8 to 10 Å), wide topology, and high (thermal,
hydrothermal, and chemical) stability. There are different criteria (pore aperture, shape of
pores, dimensionality of channel, and channel connection) according to which the
structure of zeolites can be classified. Zeolites can be found in nature or can be
synthesized. In synthesized zeolites, the pore structures are controlled by replacing
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15
negatively charged alumina with cations. Such replacement by sodium produces zeolite-
13X with a pore diameter of 8Å.
Adsorption separation of CO2 in Zeolite-13X has been studied by many
researchers. These studies were focused on three important characteristics of the
adsorption process: (i) nature of adsorption (Ward and Habgood, 1966), (ii) equilibrium
adsorption capacity (Siriwardane et al., 2005; Cavenati et al., 2005), and (iii)
breakthrough behavior (Cavenati et al., 2006). As per the study by Ward and Habgood
(1966), the dominant adsorption process in zeolite13X is physisorption and, hence, it
offers fresh adsorption capacity (when regenerated) and lower regeneration cost. As per
Siriwardane et al. (2005), zeolite13X offers the highest equilibrium adsorption capacity
among the adsorbents the tested.
The separation of molecules by zeolites as adsorbents can take place because of a
molecular sieve effect or selective adsorption. Though zeolites are known for molecular
sieving actions, separation of CO2 from a ternary gas mixture of CH4-CO2-N2 occurs due
to selective adsorption since kinetic diameter of CH4 (3.8Å), CO2 (3.3Å), and N2 (3.6Å)
are considerably less than the pore opening (8Å) of Zeolite-13X. All these three gases
get adsorbed in zeolite13X showing the highest capacity and selectivity (CO2 over CH4
or CO2 over N2) for carbon dioxide (Cavenati et al., 2004).
2.3.2 Carbon adsorbents
Carbon adsorbents are employed to absorb non-polar or weakly polar organic
molecules. They are roughly divided into four categories: (i) activated carbons (ACs), (ii)
carbon molecular sieves (CMS), (iii) activated carbon fibers (ACFs), and (iv) carbon-
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based nanomaterials such as single-walled carbon nanotubes (SWNTs) (Tagliabue et al.,
2009). Among them, ACs and CMSs are the most employed material in industrial gas
separations. Despite favorable properties, high costs of ACFs and SWNTs limit their uses
to small units. ACs and CMSs were studied for nitrogen separation from NG by, for
example, Shen et al. (2010) and Cavenati et al. (2006). They also included a comparison
with other adsorbents with respect to N2 rejection.
Activated Carbon (AC): AC is a form of carbon processed to be riddle with small,
low-volume pores that increase the surface area available for adsorption or chemical
reactions. Their usefulness is undoubtedly derived from large pore volume as well as high
surface area (Yang, 2003). These meso- or micro-porous carbonaceous materials offer
advantages over other materials in terms of cost (Choi et al., 2009). Among practical
adsorbents that are being used in industries, activated carbons are complex in terms of
both pore structure and surface chemistry due to presence of slit-shaped micropores (3 to
10Å) and oxygen (Do, 1998). The adsorption properties of activated carbon depend on
raw material and, also, on activation process (Choi et al., 2009) as well as adsorbate-
adsorbent interactions. AC performs adsorption separation by exploiting differences in
equilibrium adsorption for the constituent of a gas mixture.
Carbon Molecular Sieve (CMS): CMSs are nanoporous materials that separate
adsorbing molecules on the basis of their size and shape. A noteworthy feature of the
CMS materials is that they separate molecules on the basis of rates of adsorption (Foley,
1995). In terms of molecular sieving, CMSs are similar to zeolites with distinctive
physical structures. For example, CMSs are amorphous solids that has no long-range
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17
order while zeolites are crystalline ordered material. Another feature that sets CMSs apart
from zeolites is its variable surface chemistry (acidic/basic/neutral/radical).
2.4 Adsorption modeling
Mathematical exploration of adsorption processes traces back to work of Thomas
(1944) who studied the mechanism of ion exchange with zeolite in an ion-exchange
column. His analytical solution assumed a single solute solution. The work was then
extended to binary and multicomponent systems by Glueckauf (1949) with an assumption
of local equilibrium. With same assumption i.e. local equilibrium, Lapidus and
Amundsen (1952) examined the effects of longitudinal diffusion and incorporated first
order kinetics in their solution. In the same year (1952), Rosen published a study that
included the exact same solution of an adsorption model that introduced rate of
adsorption. He assumed that the rate of adsorption is linear.
LDF Model: The linear rate of adsorption was then explored by Glueckauf (1955)
in the form of a linear driving force (LDF) model. The LDF approximation founded the
basis for the kinetic model. Glueckauf (1955) introduced a value of 15 for the LDF
constant that provided satisfactory solutions for processes with large cycle times. For
smaller cycle times, Nakao and Suzuki (1983) proposed a graphic correlation that
provides the values of the LDF coefficient as a function of dimensionless time. Haynes
and Sharma (1975) incorporated more realistic cases of mass transfer limitations such as
film resistance, interparticle resistance, and intraparticle resistance in LDF
approximation. Serbezov and Sotirchos (1996) formulated a general methodology for the
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18
development of LDF approximations of different degrees of complexity for
multicomponent mixtures.
Particle-bed Model: The particle-bed models are the most complex models for
adsorption-based separations as they combine equations for both the bed and the particle
(Serbezov and Sotirchos, 1999). This coupled approach was first formulated by Yang and
Doong in 1985. They assumed parabolic intraparticle concentration profiles in the
solution scheme, which is equivalent to Glueckauf’s LDF approximation (Serbezov and
Sotirchos, 1999). The model equations were also solved by many others using different
numerical approaches such as orthogonal collocation (Shin and Knaebel, 1987; Lu et al.,
1992), finite element method (Kikkinides and Yang, 1993), finite difference method (Sun
et al., 1996), and global collocation (Khrisnan, 1993).
Mass Transport Model: The mass transport models used in the formulation of the
equations for the adsorbent bed and the adsorbent particles are essential parts of the
overall model. In general, there are four mechanisms of mass transport that have to be
considered: bulk diffusion, Knudsen diffusion, Knudsen flow, and viscous flow.
Serbezov and Sotirchos (1997a) showed that, in the adsorbent bed, the dominant mode of
mass transport is typically viscous flow, which can be modeled by Darcy’s law. In the
adsorbent particles, however, depending on the operating conditions, all four mechanisms
may be equally important (Serbezov and Sotirchos, 1997b). Therefore, the intraparticle
mass transport model must accurately describe the multicomponent mass transport of the
individual species over a wide range of conditions in order to be useful for simulations.
The widely applied and accepted model for the intraparticle mass transport in the
adsorption literature so far is the Fickian model, which provides a simple mathematical
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19
expression for the molar fluxes of the species. However, the Fickian model does not
account for intraparticle viscous transport and underestimates the Knudsen flow of each
species caused by total pressure gradients. For mixtures of more than two components,
the Fickian mass transport coefficient becomes an adjustable parameter that must be
obtained by fitting experimental data, even for pore structures that can be represented as
parallel pore bundles. The occurrence of viscous flow, Knudsen flow, Knudsen diffusion,
and bulk diffusion during transport of gases in porous materials is accounted for in the
dusty-gas model (Jackson, 1977; Mason and Malinauskas, 1983; Sotirchos, 1989).
Pore Diffusion Model: The bulk separation of gas mixture was first addressed by
Yang and Doong in 1985 with a pore diffusion model. They studied a 50/50 gas mixture
of methane and hydrogen in activated carbon and, then, extended it for a ternary mixture
of hydrogen, methane, and carbon dioxide (Doong and Yang, 1986). The new model, a
pore diffusion model for mass transfer, was compared to the LDF model by Farooq and
Ruthven (1990). They concluded that the pore diffusion model was complex and
computationally cumbersome and was no better than the simple LDF model.
Thermal Effects: Non-isothermal effects are intrinsic to every sorption process
because of the heat associated with adsorption and desorption. When the process takes
place in small-diameter beds with thick metallic walls, the heat is quickly transported to
the walls where it is stored, and the operation is nearly isothermal despite the presence of
heat effects. In large-diameter beds, such as the ones used commercially, the heat
produced or consumed is not conducted fast to or from the walls, and the temperature
fluctuation in the bed can sometimes be as high as 100 K (Yang, 1987). A comprehensive
discussion and experimental evidence of heat effects in large adsorbent beds is provided
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20
by Leavitt (1962). The temperature variation during adsorption and desorption can
dramatically change the performance of the adsorption-based process because the
properties of most of the adsorbents exhibit a strong temperature dependence. Therefore,
the mathematical models used for the design and optimization of adsorption-based
processes must account for the temperature changes in the adsorbent bed. Meyer and
Weber (1967) and Nagel et al. (1987) developed non-isothermal adsorption models in
which both energy equations (for the adsorbent bed and for the adsorbent particle) were
included. However, for adsorption systems with moderate heat effects and moderate
temperature dependence of the adsorption isotherms, the temperature in the particle may
be assumed to be uniform and the energy equation in the particle does not have to be
included in the model (Serbezov and Sotirchos, 1998a). Such non-isothermal models
were proposed by Chihara and Suzuki (1983), Yang and Doong (1985), and Farooq et al.
(1988).
2.5 Multicomponent separation
Separation of more than one impurity from a gas mixture requires more than one
selective adsorbent and, hence, the bed models for multicomponent separation need to
consider different adsorbents. These also create complexity for the inlet conditions for the
second adsorbent bed. Such a model has been studied by several investigators. The
arrangements of adsorbents led two types of adsorption systems: multiple adsorption
column and layered bed adsorption column systems.
Multiple Adsorption Columns: Sircar (1979) patented the first hydrogen
purification system with impurities such as CO2, CO, and CH4. Two adsorption beds
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21
were operated in series. A similar approach, a series of beds, was also patented by Kumar
(1990) for the production of hydrogen from coke oven gas by using activated carbon and
zeolite5A. Both of them kept options for independent operation of the beds, which made
the process complicated in terms of operations.
Layered Bed Adsorption Column: Chlendi and Tondeur (1995) were the first to
study fixed-bed adsorption with two layers (activated carbon and molecular sieve 5A) of
adsorbents in a single column for separation of carbon dioxide using an equilibrium
model. Chlendi et al. (1995) extended the previous work for hydrogen purification from
cracked natural gas. They neglected thermal effects for the system and studied the effects
of some operating and design variables on the performance of PSA cycles. Yang and Lee
(1998) studied adsorption dynamics of a layered bed adsorption system with activated
carbon and zeolite5A for hydrogen recovery from coke oven gas. They used a single
composition of the gas mixture and a simplified form of numerical simulation in their
study. They found an intermediate breakthrough behavior.
Later, Lee et al. (1999) extended the study and investigated the effect of the ratio
of bed heights. They found the ratio to affect the separation purity for a given throughput.
Malek and Farooq (1998) studied the removal of hydrocarbons from refinery fuel gas
with a double layered (silica gel and activated carbon) adsorption system. They pointed
out that the heat effect had a significant effect on the performance of PSA cycles.
Methane, ethane, propane, and butane were considered to be major impurities. Jee at el.
(2001) studied the effect of adsorption pressure, feed flow rate, and the ratio of
adsorbents (activated carbon to zeolite 5A) for hydrogen PSA cycles with two adsorbents
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22
(activated carbon and zeolite 5A). The notable difference with previous studies was the
inclusion of energy balance.
Takamura et al. (2001) studied a dual bed adsorption system for CO2 separation
from boiler exhaust gas. They also studied the effects of the adsorbent ratio and
concluded that the ratio affects the separation efficiency of the process. Cavenati et al.
(2006) studied separation of CO2 and N2 from a mixture of CH4, CO2, and N2. They used
a layered bed of zeolite13x and CMS 3K in their study. They investigated the
breakthrough dynamics and temperature variation in the bed. They limited their study to
two concentration combinations and a single feed pressure. They also used a fixed
volumetric flow rate in their study. Rebeiro et al. (2008) studied five component
separations in a dual bed of activated carbon and zeolite for hydrogen purification. They
compared a reduced model based on controlling resistance with complete model and
concluded that the effect of micropore resistance was not significant.
Commercial Platforms: The next level of publications on adsorption modeling
included all the features and criticality of adsorption processes together to produce a
general platform with which any process can be explored. Notable examples of such an
approach are Kumar et al. (1994) and Da Silva (1998). Based on these publications,
commercial simulators, such as Aspen Adsorption and gPROM, were built. They offer
various modeling flexibility, which can be customized for a process of interest. Even
procedures for numerical solutions can be chosen.
2.6 Numerical solution of partial differential equations
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23
Several numerical methods that address the solution of partial differential
equations (PDEs) with steep fronts and highly non-linear behaviour are available in
literature. For example, Nilchan (1997) and Nilchan and Pantelides (1998) used finite
difference and collocation methods in both time and space to discretize the PDEs, which
were then solved using a non-linear solver in the gPROMS platform. The drawbacks of
the technique include ineffective initialization of a large set of equations and a lack of
guarantee of a real-valued solution (Biegler et al., 2005). Ko et al. (2003) also stated that
complete discretization may lead to convergence failure due to the accumulation of
errors, especially for complicated models. On the other hand, the method of lines (MOL)
is a two-step technique that discretizes the space derivative first and then applies
numerical integration to find approximate solution. The decoupling of the space and time
variable can produce high-order accuracy (Biegler et al., 2005). Ko et al. (2003) found
the technique to be easier and more reliable than complete discretization models.
Discretization of Space Derivatives: Several discretization techniques (finite
difference, finite element, and finite volume) have been applied with first order or higher
order accuracy by different authors (discussed by Beigler et al., 2005) within the MOL
framework. The problem is numerical smearing or oscillation, which were addressed by
introducing a high resolution scheme (Finlayson, 1992), multiresolution scheme (Cruz et
al., 2003) and flux corrected transport (Book, 1981). The flux corrected transport method
has been modified in modern versions. For example, Van Leer used an anti-diffusion step
to avoid excessive smearing. Hirsch (1988), Webley and He (2000), and Jiang et al.
(2003) successfully used several flux limiter methods. The upwind finite differencing
method uses an adaptive or solution-sensitive finite difference stencil to determine the
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24
spread of information in a flow field. Historically, the origin of upwind methods can be
traced back to the work of Courant, Isaacson, and Rees (1952) who proposed the CIR
method. It is the preferred option because it is a good all-round performer,
unconditionally non-oscillatory, the cheapest user of simulation time, and reasonably
accurate.
Numerical Integration: The backward differentiation formula (BDF) is a family
of implicit methods for the numerical integration of ordinary differential equations. They
are linear multistep methods that, for a given function and time, approximate the
derivative of that function using information from already computed times, thereby
increasing the accuracy of the approximation. These methods are especially used for the
solution of stiff differential equations. The Gear formulae (Gear, 1971) have great
importance within the multi-step integration methods used in transient processes, since it
allows variable order and variable step change to produce high accuracy.
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25
3 Modeling and simulations of a gas adsorber
3.1 Adsorption modeling
A process simulator, namely Aspen Adsorption of Aspen Plus, was used to
simulate the adsorption of CO2 and N2 from natural gas. An adsorption model based on
the following assumptions was formulated in this simulator. The mathematical model
equations together with the correlation used for the estimation of mass and heat transfer
parameters are listed in Table 3.1.
Assumptions for physical adsorption process:
The flow pattern is described by an axially dispersed plug flow model.
The mass transfer is described by a lumped overall resistances model.
The mass transfer driving force is linear and is based on solid film.
The process is non-isothermal.
Conductivities (gas, solid, and axial conduction of wall) are negligible.
Enthalpy of adsorbed phase and enthalpy of mixing are negligible.
Heat of adsorption is constant.
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26
Table 3.1: Model equations
Ergun Equation
23
2
)1(5
1075.1
322
2)1(
31050.1
gv
ipr
gMigv
ipr
i
z
P
Component mass
balance
0
2
2
t
iq
st
iC
iz
iCg
z
iC
aDi
Gas phase energy
balance
0
04
BD
TgTwH
sTgTpafhz
gp
t
gT
gvgCbz
gT
ggvgC
Solid phase energy
balance 0011
TgTpafh
n
i t
iq
iHst
sTn
iiwpaiCs
t
sT
psCs
Wall energy balance
022
24
22
4
BDTWBD
ambTwTTWBD
ambH
BDTWBD
wTgTBD
wHt
wT
pwCw
Linear driving force
model iqiqk
t
iq
*
Mass transfer
coefficient cD
cR
pDp
KpR
fk
KpR
k 15
2
15
2
3
1
where
i
s
C
qK
.
0
0
Film mass transfer
coefficient
3/16.0
1.12
mDg
pdgg
pd
mD
fk
Film heat transfer
coefficient
3/16.0
1.12Mgk
pgCpdgg
ad
gk
fh
Wall heat transfer
coefficient
1
111.220477.026
10215.1
HPeBD
BHsphereC
HPeHPe
pd
gk
wh
Axial dispersion 12/49.973.0
prgmDiprgmDaD
Diffusion equation
23/13/1
2/11175.13
1000.1
B iVA iVP
BMAMT
ABD , M
T
macrkD 9700
Bosanquet equation
effikD
effimDpiD
,
1
,
11
Note: References for equations are included in Section 3.1.1 Model equations.
Page 43
27
3.1.1 Model equations
Momentum balance equation: The Ergun equation, which combines the
description of pressure drops in the Karman-Kozeny equation for laminar flow and the
Burke-Plummer equation for turbulent flow, is useful for both laminar and turbulent flow
(Bird et al., 1960).
2
g3
ip
gi
5
g3
i
2
p
2
i
3
vr2
M)1(1075.1v
r2
)1(1050.1
z
P
(3.1)
where P is feed pressure (bar), z is the height of the adsorbent bed, εi is the interparticle
Voidage, νg is the gas velocity (m/s), ψ is the shape factor, μ is the dynamic viscosity (N
s/m2), M is the molecular weight (kg/kmol), and rp is the particle radius (m).
Mass balance equation (ref: Aspen manual): The transfer of mass from gas to a
solid surface can occur in four ways: dispersion, convection, accumulation, and diffusion.
Dispersion may happen in radial or axial directions. Radial dispersion was not considered
in this model.
0
2
2
t
q
t
C
z
C
z
CD i
si
b
igiai
(3.2)
where Ci is the molar concentration of component i (kmol/m3), Da is the axial dispersion
coefficient of component i (m2/s), εi is the interparticle voidage, εb is the bed voidage, t is
the time (second), ρs is the adsorbent bulk density (kg/m3), and qi is the loading
(kmol/kg).
Gas phase energy balance (ref: Aspen manual): The gas phase energy balance
includes the convection of energy, accumulation of heat, compression, heat transfer from
gas to solid, and heat transfer from gas to the internal wall. Conductive heat transfer of
gas has not been considered.
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28
0TTD
H4TTah
zp
t
TC
z
TC 0g
B
wsgpf
gg
gvgB
g
ggvg
(3.3)
where Cvg is the specific gas phase heat capacity at constant volume (MJ/kmol/K), ρg is
the gas phase molar density (kmol/m3), Tg is the gas phase temperature (K), Ts is the solid
phase temperature (K), To is the ambient or wall temperature according to context use
(K), hf is the gas-solid heat transfer coefficient (MW/m2/K), ap is the specific particle
surface per unit volume bed (m2 (Particle area)/m
3 (Bed)), Hw is the gas-wall heat transfer
coefficient (MW/m2/K) and Db is the bed diameter (m).
Solid phase energy balance (ref: Aspen manual): The solid phase energy balance
includes the accumulation of heat, accumulation of enthalpy in the adsorbed phase, heat
of adsorption, and gas-solid heat transfer from gas to solid through the film at the solid
surface. The heat transfer area was assumed to be proportional to the area of the
adsorbent particles. The conductive heat transfer from the solid was not considered for
this application.
0TTaht
qH
t
TwC
t
TC 0gpf
n
1i
iis
sn
1i
ipaiss
pss
(3.4)
where Cps is the specific heat capacity of adsorbent (MJ/kmol/K), Cpai is the specific heat
capacity of the adsorbed phase (MJ/kmol/K), wi is the solid phase concentration
(kmol/kg), and ΔHi is the heat of adsorption of component i (MJ/kmol).
Wall energy balance (ref: Aspen manual): The wall energy balance includes heat
accumulation within the wall material, heat transfer from the bed to the inner wall, and
heat transfer from the outer wall to the environment.
0DWD
TTWD4H
DWD
TTD4H
t
TC
2
B
2
TB
ambw
2
TBamb2
B
2
TB
wgB
ww
pww
(3.5)
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29
where, Cpw is the specific heat capacity of column wall (MJ/kg/K), ρw is the wall density
(kg/m3), WT is the width of column (m), Tw is the wall temperature (K), Tamb is the
ambient temperature (K), and Hamb is the wall-ambient heat transfer coefficient
(MW/m2/K).
Linear driving force (LDF) model: The concentration difference between bulk
gas and the solid phase sets the mass transfer driving force (mass transfer coefficient).
One model that has found wide and successful use in the analysis and design of
adsorptive separation processes is known as the linear driving force (LDF) model
(Alvarez-Ramirez et al., 2005). This first order model was proposed by Gleuckauf and
Coates (1947) for adsorption chromatography. The model is simple, analytical, and
physically consistent (Sircar and Hufton, 2000) and realistically represents an industrial
process (Biegler et al., 2005).
i
*
ii qqk
t
q
(3.6)
where q is the average adsorbate concentration in the solid (kmol/kg), q* is the
instantaneous equilibrium concentration, and k is the effective mass transfer coefficient of
component i.
Isotherm Model (ref: Aspen manual): The temperature-dependent Langmuir-
Freundlich isotherm (adsorption equilibrium at fixed temperature) model was used in this
study. This isotherm takes the advantages of monolayer adsorption, described by the
Langmuir model for low pressure, and multilayer adsorption, described by the Freundlich
model for high-pressure adsorption. The multicomponent adsorption equilibria were
introduced through the ideal adsorption solution theory (IAS). The Langmuir-Freundlich
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30
model for a temperature-dependent multicomponent system was presented in Aspen
Adsorption as:
1
sT
6a
e3a
iP
5a1s
T
4a
e3a
iP
2a
1aiq
(3.7)
where a1, a2, a3, a4, a5, and a6 are constants and Pi is the partial pressure of component i.
Mass transfer coefficient: There are three mass transfer resistances in an
adsorption column: film resistance, macropore resistance, and micropore resistance.
Through a moment analysis of the pulse response from a chromatographic column model,
Haynes and Sharma (1975) came up with following equation. The mass transfer
coefficient obtained from this equation was used in the LDF model.
c
c
pp
p
f
p
D
R
D
KR
k
KR
k 15153
122
(3.8)
where kf is the film mass transfer coefficient (m/s), Dp is the pore diffusivity/macropore
diffusivity (m2/s), Rc is crystal radius (m), Dc is crystal diffusivity/micropore diffusivity
(m2/s), and K is dimensionless Henry’s Constant.
For the nonlinear system, it works with reasonable accuracy when Henry’s
constant is replaced by q0/C0, where C0 is the feed concentration of the adsorbate in the
gas phase, and q0 is the corresponding equilibrium in the adsorbed phase (Hassan et al.,
2008). The constant (K) must be in a dimensionless form:
i
s
0
0
i
sH .
C
qKK
(3.9)
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31
where KH is Henry’s constant, q0 is initial solid phase concentration, and C0 is initial bulk
concentration.
Film mass transfer coefficient: The mass transfer coefficient for a stagnant film
surrounding a solid adsorbent packed inside a fixed-bed adsorber was calculated from the
following correlation (Wakao and Funazkri, 1978):
3/16.0 ScRe1.12Sh (3.10)
where Sh is the Sherwood Number
m
pf
D
dk, dp is the particle diameter, Dm is the
molecular diffusivity, kf is the film mass transfer coefficient, Sc is the Schmidt Number
mg D
and Re is the Reynolds Number
gpgdv.
The calculation of this film mass transfer coefficient requires physical properties
of fluids. For a gas mixture, the following correlations (Griskey, 2002) were used to
determine mixture properties. The correlation of Fuller et al. (1966) was used for the
calculation of binary diffusivity, which works for both polar and non-polar molecules.
The diffusivities were then corrected for tortuosity as suggested by Do (1998) and then
component diffusivity was calculated using Wilkes’ formula (Equation – 3.13; as
explained by Do, 1998)
n
i
iimix y1
(3.11)
n
1in
1j
ijj
iimix
y
y
(3.12)
Page 48
32
24/12/12/1
1122
1
i
j
j
i
j
iij
M
M
M
M
(3.13)
23/1
B i
3/1
A i
2/1
BA
75.13
AB
VVP
M
1
M
1T1000.1
D
(3.14)
B,A2
pCorr
AB DD
(3.15)
1
1 ,
, )1(
n
ABB
corr
BA
BA
eff
imD
yyD (3.16)
where ρmix is the density of the gas mixture, μmix is the viscosity of the gas mixture, yi is
the mole fraction of component i and φij the viscosity of component i and j, DAB is the
binary diffusivity (cm2/sec) of component A and B, Vi is the atomic diffusion volumes
(cm3), eff
imD ,
is the effective component molecular diffusivity, corr
BAD , is corrected binary
diffusivity, and τ is tortuosity
Pore diffusion in macropore: Diffusion in gases is the result of the collision
process (Bird et al., 1960). In a macropore, two types of collision take place, which
results in two types of diffusivities: molecular diffusivity (collision between molecules)
and Knudsen diffusivity (collision between molecules and the pore wall). Depending on
the mean free path of gas molecules and pore diameter, one diffusion process may
dominate over others. The effect can be qualitatively predicted by using the concepts of
the Knudsen number and mean free path as outlined by Do (1998). Molecular diffusivity
has already been discussed in a previous section. Knudsen diffusivity can be calculated
using Equation 3.17 as presented by Smith (1970) and is valid for a capillary tube.
Page 49
33
Equation 3.18 was suggested by Do (1998) for effective Knudsen diffusivity in porous
media. Pore diffusivity (Equation 3.19) is the combined effect of molecular and Knudsen
diffusivity. It can be calculated using the Bosanquet Equation (Cavenati et al., 2006):
M
Tr9700D mack (3.17)
k2
beff
k DD
(3.18)
eff
i,k
eff
i,mpi D
1
D
1
D
1 (3.19)
where Dk is the Knudsen diffusivity, rmac is the macropore radius, Dkeff
is the effective
Knudsen diffusivity, and Dpi is pore diffusivity of component i.
Axial dispersion: The axial dispersion coefficient (Da) varies along the length of
the bed. Aspen Adsorption estimates the values during the simulation using the following
correlation:
1
pgmipgma r2/D49.9rD73.0D
(3.20)
Film heat transfer coefficient: The correlation published by Wakao and Funazkri
(1978) was used in the calculation of the film heat transfer coefficient. This equation also
counts for dispersion effects:
1/3Pr0.61.1Re2.0Nu (3.21)
where Nu is the Nusselt number
g
af
k
dh, Pr is the Prandtl number
Mk
C
g
pg
and da is the
diameter as an agglomerate (Do, 1998).
Gas-Wall heat transfer coefficient: The determination of gas-wall heat transfer is
critical since the exact nature of contact between solid particles and the wall is unknown.
Page 50
34
Kast (1988) graphically represented the relationship. The following correlation uses
results from the graphical representation given by Kast (1988). The value obtained has
been used as model input.
1
26 111.220477.010215.1
HB
Bsphere
HH
p
g
wPeD
HCPePe
d
kh (3.22)
where Csphere is 12 for a packed bed of spheres, PeH (1.15dpνgρgMCpg/kg) is the Péclet
number for gas wall heat transfer, and kg is the conductivity of the gas phase (MW/m/K).
Wall-ambient heat transfer coefficient: This coefficient should follow the exact
environment in which the experiments were performed. Air or water is generally used as
an external cooling medium and the heat transfer coefficient for air and water are 10-100
W/m2/K and 500-10000 W/m
2/K, respectively.
Heat of adsorption: The heat arising due to the adsorption of a certain amount of
molecules is known as the heat of adsorption. Though many forms of heat of adsorption
have already been discussed in the literature, isosteric heat of adsorption directly
describes the non-isothermal behavior of adsorption systems (Sircar et al., 1999). This
key thermodynamic variable plays an important role in the design of adsorption systems
because it changes the adsorbent temperature.
3.1.2 Solution of model equations
The model equations were solved numerically using the method of line (MOL)
technique, a built-in method in Aspen Adsorption. This two-step technique discretized
the space derivative first and then applied numerical integration to find an approximate
solution. The space derivatives were set to discretize by using the upwind finite
Page 51
35
difference method. The method offers good all-round performance. Numerical
integrations were performed using Gear formulae (Gear, 1971). The formulae use the
implicit backward differentiation technique.
3.1.3 Calculation procedure
The basic inputs required for starting the calculations are: the physical properties
of the column and adsorbents, feed conditions, mass transfer, heat transfer, and isotherm
parameters. Some of these inputs were fixed while some others varied with operating
conditions. For example, the porosity of adsorbent was fixed during the study, while
mass transfer parameters changed with operating conditions. The mass and heat transfer
parameter can be obtained using equations described in section 3.1.2. These equations
also require the physical properties of feed gases. In this study, the NIST (National
Institute of Standard and Technology) database was used for obtaining the physical
properties of CH4, CO2, and N2. Aspen Adsorption’s NIST thermo engine has access to
this database.
Figure 3.1 shows the inputs for a single-bed adsorption column. A layer bed
column, for example, with 2 layers of different adsorbent requires 2 sets of properties for
adsorbents. The introduction of a two-adsorbents layer will also influence the overall
flow passage for the feed. The number of parameters for the isotherm depends on the
isotherm model. For example, the Langmuir model is comprised of two parameters, while
the Langmuir-Freundlich model is comprised of six parameters for each component of
feed. Aspen starts the calculation assuming an initial velocity. A dynamic run produces
product composition in every time interval. The feed and product information was then
Page 52
36
processed to determine the amount of adsorbent and separation efficiency, which are
defined below.
Amount of adsorbent refers to the following relationship:
Amount of adsorbent, tF
Mw
mol
kg (3.23)
where, M is the mass of adsorbent (kg), F is the feed flow rate, and t is the cycle time (s).
Separation efficiency refers to the amount of nitrogen or carbon dioxide adsorbed
in the adsorbent. It was defined as:
Separation efficiency, 100
in
outins
n
nn (%) (3.24)
where n is the number of moles of nitrogen or carbon dioxide.
Page 53
37
Figure 3.1: Calculation procedure
Input
Feed
Pressure
Temperature
Composition
Flow rate
Column
Radius
Porosity
Specific heat
Wall thickness Flow rate
Adsorbent Pressure
Bed length Temperature
Bulk density Composition
Bulk porosity
Extrude radius
Extrude density
Extrude porosity Amount of adsorbents
Transport Parameters Separation efficiency
Mass Transfer coefficient Correlations
Heat transfer coefficient
Heat of adsorption
Specific heat
Thermal conductivity
Isotherm parameters
Product
Post Processing
Aspen Adsorption
Simulator Output
Page 54
38
3.2 Model validation
The model was validated against three different separation systems that covered
pure and multicomponent feeds, homogeneous and heterogeneous adsorbents, isothermal
and non-isothermal heat balance, a wide pressure range, and a wide range of
concentrations of adsorbate to ensure the versatility of the model. The systems were as
follows: N2 separation from helium using activated carbon as per Shen et al. (2010), CH4
separation from hydrogen using Zeolite 5A as per Bastos-Neto et al. (2010), and CO2
separation from a mixture of CH4, CO2, and N2 using zeolite13X as per Cavenati et al.
(2006). The operating boundaries, such as feed pressure, for these three systems varied
widely (1.0-20.2 bar), though the temperature range is quite narrow (300-303 K). The
concentration of adsorbate in feed varied from 0.5 to 20 mol %. This operating window
reflected the likely feed conditions such as pressure, temperature, and composition of a
typical natural gas transmission pipeline.
3.2.1 Nitrogen separation using activated carbon
Shen et al. (2010) reported several experimental breakthrough behaviours of N2 in
pitch-based activated carbon beads (ACB) in diluted conditions (0.5% N2 and 0.995%
helium) at 1 bar and for a wide range (303-423 K) of temperatures. The breakthrough
curve at 303K, as it is close to the temperature of natural gas pipelines, was selected for
comparison and was compared with the simulated breakthrough curve obtained from the
proposed model. The inputs for the model are summarized in Table 3.2. The physical
properties of the adsorbent were taken from the literature. The mass transfer coefficient
was calculated and isotherm parameters were obtained from the fitting of the Langmuir
Page 55
39
isotherm, which fitted the experimental data with an average absolute deviation (AAD) of
1.94%. Only two constants of the isotherm model were used because the separation
process represents single component separation in a diluted condition. Heat transfer
parameters were omitted from the input table as the process was isothermal. Figure 3.2 is
a comparison of the experimental and simulated results of authors to model the output of
this work. The plots portray the accuracy of the model in terms of both, shape and width
of the breakthrough curves. The AAD between experimental data and model output (our
study) is 3.1% and that of their model is 2.9%. This thereby validates the model.
Page 56
40
Table 3.2: Model input (N2-ACB system)
Descriptions Value
Pressure (bar) 1
Temperature (K) 303
Concentration of nitrogen (% mole) 0.5
Concentration of helium (% mole) 95.5
Height of adsorbent layer (m) 0.165
Internal diameter of adsorbent layer (m) 0.0093
Inter-particle voidage (m3 void/m
3 bed) 0.32
Intra-particle voidage (m3 void/m
3 bed) 0.51
Bulk solid density of adsorbent (kg/m3) 669
Adsorbent particle radius (m) 5.45E-04
Adsorbent shape factor ( ) 1
Constant mass transfer coefficients (1/s) 0.48
Isotherm parameter, a1 (n/a) 3.31E-04
Isotherm parameter, a2 (n/a) 0.0977
Note: Langmuir isotherm model was used.
Page 57
41
Figure 3.2: Breakthrough concentration profiles of N2 in pitch-based AC beads (0.5% N2
in helium at 303K and 1 bar) under isothermal conditions
0.00
0.20
0.40
0.60
0.80
1.00
0 100 200 300 400
Mo
le ra
tio
of
N2
at
bed
ex
it (
C/C
0)
Time (second)
Experiment
(Shen et al.,
2010)
Simulation
(This Study)
Page 58
42
3.2.2 Methane separation from hydrogen using zeolite 5A
Bastos-Neto et al. (2010) presented a series of adsorption isotherms of CH4 and
breakthrough curves on one zeolite 5A at various concentrations, temperatures, and
pressure conditions. They used a mixture of CH4 and H2 to analyze the recovery of CH4
from H2. From those breakthrough curves, a high pressure at 20.2 bars on the
breakthrough curve was selected to check the high-pressure response of our model and to
determine the CH4 handling capability of the model at a moderate concentration of
adsorbate (8.8 mol % CH4, balance H2) and high pressure. Inclusion of zeolite 5A also
helped to test various adsorbent handling capability of the model.
The inputs of the model are summarized in Table 3.3. Heat transfer parameters
are not included in Table 3.3 because the system is isothermal. Physical properties of
adsorbents and column dimensions were obtained from the literature to match the
experimental arrangements used by Bastos-Neto et al. (2010). The experimental
adsorption data obtained from the literature were fitted with the Langmuir-Freundlich
isotherm. The isotherm model fitted the experimental adsorption data with an AAD of
3.23%. Mass transfer parameters were calculated using the correlations mentioned in this
work (Section 3.1.2).
Figure 3.3 portrays experimental and simulated breakthrough profiles. The shape
and width of the breakthrough curve proved the accuracy of our model. The average
absolute deviation between experimental data and model output were 5.75%. This
comparison especially highlights the capability of the model in handling moderate
concentrations of contaminant such as 8.8 mole percent CH4 in the feed at high pressure.
Page 59
43
Table 3.3: Model inputs (CH4-H2-Zeolite5A system)
Descriptions Value
Pressure (bar) 20.2
Temperature (K) 300
Concentration of methane (% mole) 8.8
Concentration of hydrogen (% mole) 91.2
Height of adsorbent layer (m) 0.08
Internal diameter of adsorbent layer (m) 0.022
Inter-particle voidage (m3 void/m
3 bed) 0.44
Intra-particle voidage (m3 void/m
3 bed) 0.41
Bulk solid density of adsorbent (kg/m3) 706
Adsorbent particle radius (m) 0.001
Adsorbent shape factor 1
Constant mass transfer coefficients (1/s) 0.01
Isotherm parameter, a1 (n/a) 7.8E-04
Isotherm parameter, a2 (n/a) 0.1895
Note: Data were obtained from Bastos-Neto et al. (2010).
Page 60
44
Figure 3.3: Breakthrough concentration profile of methane in Zeolite 5A (8.8% Methane
in Hydrogen at 303 K and 20.2 bar) under isothermal conditions
0.00
0.20
0.40
0.60
0.80
1.00
0 1200 2400 3600 4800 6000
Mo
le r
ati
o o
f C
H4
at
bed
ex
it (C
/C0)
Time (second)
Simulation (This
Study)
Experiment
(Bastos-Neto et al.
(2010))
Page 61
45
3.2.3 Carbon dioxide separation using Zeolite 13X
The separation of CO2 from a mixture of CH4, CO2, and N2 was studied by
Cavenati et al. (2006) using zeolite13X. This ternary gas mixture (70 mol % CH4, 20 mol
% CO2, and 10 mol % N2) reflects the likelihood of components as well as their
concentrations in natural gas and enforces the inclusion of multicomponent non-
isothermal behavior, a more practical phenomenon in gas separation industries, in the
model. The study was performed at three different temperatures (298K, 308K, and
323K). A temperature-dependent isotherm model, the Langmuir-Freundlich, was used to
relate the equilibrium data. The breakthrough behaviors of the system were evaluated
using the data provided by the authors.
The inputs used for this system are summarized in Table 3.4. Isotherm parameters
are in Table 3.5. Some transport properties were calculated using the
equations/correlations discussed in section 3.1.1. The results of our model were presented
graphically in Figures 3.4 – 3.5. The column dynamics, i.e., the breakthrough and
temperature profiles, were compared in Figures 3.5 – 3.6. Breakthrough dynamics differ
by 2.1% (AAD), while temperature profiles differ by 0.7% (AAD) when compared to the
experimental data. The cooling side of the temperature profile notably differs from the
experimental data. This might be due to the end effect on the temperature probe that was
placed between two layers of adsorbent. The model fairly describes the non-isothermal
behaviour associated with the removal of CO2 with a relatively high concentration. It is
also capable of handling multicomponent gas and the temperature dependency of the
isotherm.
Page 62
46
Table 3.4: Model inputs (CH4-CO2-N2-zeolite13X system)
Description Value
Pressure 2.5
Temperature 300
Height of adsorbent layer (m) 0.20
Wall thickness (m) 0.0024
Internal diameter of bed (m) 0.016
Inter-particle voidage 0.33
Intra-particle voidage 0.46
Bulk density (kg/m3) 715.00
Particle radius (m) 9.00E-04
Specific heat capacity (J/kg/K) 880.00
Wall specific heat capacity (J/kg/K) 500.00
Heat transfer coefficient (W/m2/K)
overall 67.00
gas to wall 192.00
wall to ambient 37.00
Wall thermal conductivity (W/m/K) 13.40
Wall density (kg/m3) 8238.00
Mass transfer coefficients (1/s)
CH4 3.49E-05
CO2 7.26E-03
N2 4.74E-03
Heat of adsorption (MJ/Kmol)
CH4 -38.95
CO2 -38.95
N2 -15.93
Page 63
47
Table 3.5: Isotherm parameters (CH4-CO2-N2-zeolite13X system)
Component Parameter Value
CH4
a1 1.71E-04
a2 1.72E-04
a3 7.16E-01
a4 3.19E+03
a5 1.06E-05
a6 2.98E+03
CO2
a1 4.98E-04
a2 1.05E-02
a3 4.92E-01
a4 2.16E+03
a5 1.47E-03
a6 2.04E+03
N2
a1 3.37E-06
a2 8.71E-01
a3 7.96E-01
a4 1.46E+03
a5 1.06E-03
a6 1.36E+03
Page 64
48
Figure 3.4: Breakthrough concentration profiles of 70 mol % CH4, 20 mol % CO2 and 10
mol % N2 in Zeolite 13X at 300K and 2.5 bars
0.00
0.25
0.50
0.75
1.00
0 400 800 1200 1600 2000 2400
Mo
le R
ati
o o
f C
H4,
CO
2a
nd
N2
at
bed
ex
it (
C/C
0)
Time (seconds)
CH4 (Experiment by Cavenati et al., 2006)
Simulation,CH4 (This Study)
CO2 (Experiment by Cavenati et al., 2006)
Simulation, CO2 (This study)
N2 (Experiment by Cavenati et al., 2006)
Simulated, N2 (This Study)
Page 65
49
Figure 3.5: Temperature profile at bed exit (70 mol % CH4, 20 mol % CO2 and 10 mol %
N2 in Zeolite 13X at 300 K and 2.5 bars)
295
300
305
310
315
320
325
330
335
0 400 800 1200 1600 2000 2400
Tem
pera
ture a
t b
ed
ex
it (
K)
Time (second)
Simulation (This
study)
Experiment (Cavenati
et al., 2006)
Simulation (Cavenati
et al., 2006)
Page 66
50
4 Results and Discussion
4.1 Description of simulated gas adsorption systems
This work simulated the adsorption of CO2 and N2 from natural gas containing
50-90% CH4, 5-25% CO2, and 5-25% N2 in layered bed adsorbers. As depicted in Figure
4.1, the layered bed adsorber contains two layers of selected adsorbents, namely
zeolite13X and activated carbon (ACB) or a carbon molecular sieve (CMS3K). All these
adsorbents can adsorb CH4, CO2, and N2. However, zeolite13X has greater adsorption
capacity with CO2 than CH4 and N2 (Cavenati et al., 2004). ACB and CMS3K also
preferentially adsorb CO2 over N2. Thus, zeolite13X is placed at the bottom of the
adsorber where the gas feed was introduced to completely remove CO2 and ACB, or
CMS3K is placed at the top to remove N2.
A single column was filled with two adsorbents. First, the amount of zeolite13X
was adjusted to have a CO2 breakthrough at the desired cycle time. Then, amount of
ACB/CMS3K were adjusted in steps to obtain a nitrogen separation efficiency of over
90%. Two cycle times were used: 80 seconds for zeolite13X-CMS3K to implement
kinetic preference of CMS3K for N2 over CH4 and 600 seconds for zeolite13X-ACB to
implement equilibrium adsorption of N2 in ACB. The transport parameters were adjusted
(Appendix – A) to maintain a simplified model without sacrificing the rigour of the
model. Adsorption equilibrium information and physical properties of zeolite13X and
CMS3K were obtained from Cavenati et al. (2004 and 2006) and that of ACB were
obtained from the work of Shen et al. (2010).The heat transfer coefficient between the
wall and environment was obtained from the work of Cavenati et al. (2006).
Page 67
51
Figure 4.1: Double bed adsorber
Product
Feed
Page 68
52
4.2 Simulation results for zeolite13X
Simulations were carried out on single-bed zeolite13X for different feed pressures
and compositions for complete separation of CO2. Five different feed pressures (2.5 bars,
5 bars, 10 bar, 20 bars, and 30 bars) were analyzed. Concentration of CO2 and N2 were
varied from 5 to 25%. The amount of CH4 was kept constant at 70%. The inputs are
presented in Tables 4.1 and 4.2. These inputs were for feed containing 70% CH4, 20%
CO2, and 10% N2 at 2.5 bars and 300K. The feed flow rate was 1.6 SLPM. Some of the
inputs, for example mass transfer coefficients, were calculated for every concentration
and every pressure. The isotherm parameters were obtained by fitting the experimental
adsorption data (Cavenati et al., 2004) and were kept unchanged. Physical properties of
zeolite13X were obtained from the work of Cavenati et al. (2006). The wall to ambient
heat transfer coefficient was adjusted to obtain the temperature profile published by
Cavenati et al. (2006).
The height of the adsorber bed was varied to get the breakthrough of CO2 at the
desired cycle time. The breakthrough implies the optimum amount of zeolite13X needed
for 100% separation of CO2. The amount (gram per mole of feed) is presented in Figure
4.2 as a function of feed pressure and concentration of CO2.
Page 69
53
Table 4.1: Physical properties of zeolite13X and properties of column
(Cavenati et al., 2006)
Column Zeolite13X
Height of adsorbent layer/column, m 0.2 0.2
Wall thickness of column, m 0.0024
Internal diameter of column, m 0.016
Density of column wall, kg/m3 8238
Inter-particle voidage/column porosity 0.33 0.33
Specific heat capacity, J/kg/K 500 920
Bulk density/column density, kg/m3 756 756
Thermal conductivity of column wall, W/m/K 13.40
Particle/extrude density of zeolite13X 1130
Particle/extrude radius of zeolite13X, m 0.008
Intra-particle voidage/extrude porosity 0.54
Extrude tortuosity 2.2
Page 70
54
Table 4.2: Parameters used in simulation for zeolite13X
Total Pressure, bar 2.5, 5, 10, 20, 30
Flow rate, SLPM 1.6
Temperature, K 300
Mass transfer coefficient, 1/s CH4 – 0.3315
CO2 – 0.0165
N2 – 0.5053
Heat transfer coefficient, W/m2/K Gas-Solid – 60
Gas-wall – 36
Wall-ambient – 192
Isotherm parameters for CH4 a1 – 0.0112
a2 – 0.00029
a3 – 0.834
a4 – 1590
a5 – 0.00037
a6 – 1610
Isotherm parameters for CO2 a1 – 0.00033
a2 – 0.0021
a3 – 0.43
a4 – 2850
a5 – 0.0031
a6 – 2450
Isotherm parameters for N2 a1 – 0.0022
a2 – 0.00042
a3 – 0.885
a4 – 1740
a5 – 0.0001
a6 – 1970
Note: Transport coefficients were calculated (70%CH4/ 20%CO2/10% N2/2.5bar/300K).
Page 71
55
Figure 4.2: Required amount of zeolite13X for complete separation of CO2 as a function
of feed pressure
0
10
20
30
40
50
60
70
80
90
100
0 5 10 15 20 25 30
Am
ou
nt
of
zeo
lite
13
X
(g/m
ol o
f fe
ed
ga
s)
Feed gas pressure (bar)
05%CO2 - 25% N210%CO2 - 20% N215%CO2 - 15% N220%CO2 - 10% N225%CO2 - 05% N2
Page 72
56
4.2.1 Parametric study
Parametric studies were performed to determine the effect of feed conditions on
adsorption of CO2 and N2. Two effects were determined. They are (i) the effect of feed
pressure and (ii) the effect of concentration.
Effect of feed pressure: As per figure 4.2, CO2 adsorption capacity of zeolite13X
increases in low pressure ranges (2.5 to 5 bars), while capacity decreases in high pressure
ranges (10 to 30 bars). This reversal of adsorption capacity occurs for feed pressure
ranging from 5 to 10 bars. The effect of feed pressure becomes less significant at the
pressure range of 20 to 30 bars. The possible reason behind this reversal of adsorption
capacity could be multicomponent adsorption in zeolite13X; more specifically, selective
adsorption of CO2 over N2 might play the significant role. To further investigate this, the
adsorption capacities presented in Figure 4.3b were determined using the Langmuir-
Freundlich model, while the selectivity (Figure 4.3a) was obtained from the graphical
representation. As expected, N2 adsorption capacity of zeolite13X is low (0.05 mol/kg)
for a low partial pressure (0.13 bar) and high (1.44 mol/kg) for a high partial pressure
(7.50 bar) of N2. However, selective adsorption of CO2 over N2 is high (37.1) at a low
partial pressure (0.13 bar) and low (0.30) at a high partial pressure (7.50 bar) of CO2.
This reversal of selectivity implies that N2 was preferentially adsorbed in zeolite13X at a
high concentration of N2. The increased adsorption of N2 on zeolite13X is presented in
Figure 4.5 as a function of feed pressure. As presented, less of 10% (mole) of total N2
was adsorbed at 2.5 bars, while the amount exceeds 40% at 30 bars.
Page 73
57
a) Selectivity of CO2 over N2
b) CO2 or N2 adsorption capacity (mol/kg) of zeolite13X
Figure 4.3: Adsorption capacities and selectivity for CO2-N2-zeolite13X system
0
5
10
15
20
25
30
35
40
0 1 2 3 4 5 6 7 8
Sele
cti
vit
y o
f C
O2
over
N2
Partial pressure of CO2 (bar)
0
1
2
3
4
5
6
7
0 1 2 3 4 5 6 7 8
Ad
sorp
tion
cap
aci
ty o
f C
O2
or
N2
(mo
l/k
g)
Partial pressure of CO2 or N2
CO2
N2
Page 74
58
Effect of concentration of CO2 and N2: The amount of zeolite13X needed for
100% separation of CO2 is presented in Figure 4.4. Since the concentration of CH4 was
fixed, a low concentration of CO2 implies a high concentration of N2 and vice versa. The
amount of zeolite13X increases linearly for all concentrations of CO2 at 2.5 bars. The
trend is similar for 5 bars but deviates from linearity in 10, 20, and 30 bars. When
compared to the amount of required at 2.5 bars, the required amount of zeolite13X is less
at 5 bars for all concentrations of CO2. At 10 bars, the trend is true for higher
concentrations (above 10%) of CO2. A high amount of zeolite is needed, when compared
to 2.5 to 10 bars, at 20 bars and above for low concentrations (less than approximately
15%) CO2. The behaviour can be explained in terms of selective adsorption, as explained
before (see the effect of feed pressure). Selective adsorption of N2 over CO2 implies that
more N2 will be adsorbed. Figure 4.5 shows that high N2 efficiency was obtained at high
feed pressure and high concentration of N2.
Page 75
59
Figure 4.4: Effect of concentration (%) of CO2 on required amount of zeolite13X for
100% separation of CO2
0
10
20
30
40
50
60
70
80
90
100
0 5 10 15 20 25 30
Am
ou
nt
of
zeo
lite
13
X
(g/m
ol o
f fe
ed
ga
s)
Concentration of CO2 (%)
Feed pressure
2.5 bar 5.0 bar
10.0 bar 20.0 bar
30.0 bar
Page 76
60
Figure 4.5: N2 separation efficiency of zeolite13X
0
5
10
15
20
25
30
35
40
45
50
0 5 10 15 20 25 30 35
N2
sep
ara
tio
n e
ffic
ien
cy
(%
)
Feed pressure (bar)
25% N220% N215% N210% N25% N2
Page 77
61
4.2.2 Correlation to determine amount of zeolite13X
The amounts of zeolite13X determined from the feed pressures were correlated in
a single equation:
1094
654
)1(87
)1()32(1CCC
CCC
yyPCC
yyPCCCQ
4.1
where Q is the amount of adsorbent, P is the feed pressure, y is the mole fraction of N2 or
CO2, and C1 to C10 are parameters. The correlation determines the total amount of
zeolite13X depending on feed pressure. The parameters (C1 to C10) are shown in Table
4.3. There are 2 sets of parameters listed in this table for two pressure ranges. The mole
fraction (y) in the correlation refers to the mole fraction of CO2 in the feed stream, and
the separation factor (s) in the correlation was 1 as the zeolite13X removed all (100%)
carbon dioxide from the feed.
Figure 4.6a presents a comparison of the predicted results for low feed pressures
(2.5 to 10 bar). The average absolute deviation (%) that was observed for this feed stream
was 1.3%. The maximum absolute deviation was 5.6% for the feed stream that carried
05% carbon dioxide at 5 bars. Figure 4.6b compares the predicted results for high feed
pressures (10 to 30 bar). The average absolute deviation (%) that was observed for this
feed stream was 0.36 %. Maximum absolute deviation was observed for the feed stream
that carried 10% carbon dioxide at 10 bars. The predicted amount of zeolite13X in the
feed conditions was lower by 1.15 wt. %.
Page 78
62
Table 4.3: Parameters of correlation for determination of amounts of zeolite13X
Parameter Feed pressure
<10 bar ≥ 10 bar
C1 1.559 2.639
C2 404.474 -3.344
C3 0 2.653
C4 13.203 0.84
C5 0.505 -0.107
C6 -0.61 -7.951
C7 3.843 1.188
C8 0 0.111
C9 0.354 0.107
C10 1.01 -7.014
Page 79
63
(a) Feed pressure 2.5 to 10 bars
(b) Feed pressure 10 to 30 bars
Note: Simulated means results obtained from Aspen Adsorption while
predicted means results obtained from empirical correlation
Figure 4.6: Comparison of simulated and predicted amounts of zeolite13X
0
20
40
60
80
100
0 20 40 60 80 100
Pre
dic
ted
am
ou
nt
of
zeo
lite
13
X
(g/m
ol
of
feed
)
Simulated amount of zeolite13X
(g/mol of feed)
5% CO2
10% CO2
15% CO2
20% CO2
25% CO2
0
20
40
60
80
100
0 20 40 60 80 100
Pre
dic
ted
am
ou
nt
of
zeo
lite
13
X
(g/m
ol
of
feed
)
Simulated amount of zeolite13X
(g/mol of feed)
5% CO2
10% CO2
15% CO2
20% CO2
25% CO2
Page 80
64
4.3 Simulation results for zeolite13X-CMS3K system
Simulations were performed for various feed conditions using a layered bed of
zeolite13X-CMS3K. The obtained data were then processed to determine the amount of
adsorbents and adsorbed N2. The system adsorbed all CO2 in zeolite13X. Four pressure
stages (2.5 bars, 5 bars, 7.5 bars, and 10 bars) were studied using 15-25% N2, 10-20%
CO2, and 55-75% CH4. The concentrations of N2 and CO2 were varied in 10% intervals.
The study was performed for a cycle time of 80 seconds.
Sample inputs for the system are presented in Tables 4.4 and 4.5. The amount of
zeolite13X was adjusted to adsorb all the CO2 from the feed before starting the
simulation of the dual bed adsorption column. The amount of this zeolite13X was kept
fixed for particular feed condition, while the amount of CMS3K was varied to get a N2
separation efficiency ranging from 50 to 95%. No attempt was made for 100% removal
of N2. Since all CO2 was adsorbed in zeolite13X, this discussion will be limited to N2
separation efficiency only. The total amount of adsorbents needed for the removal of CO2
and N2 has been plotted in Figure 4.7. Figure 4.7 shows amount of zeolite13X and
CMS3K as function of feed pressure and concentration and N2 separation efficiency. An
increase in N2 separation efficiency required more CMS3K while an increase in feed
pressure required less CMS3K. The effects of concentration of N2 were not significant.
Page 81
65
Table 4.4: Physical properties of double bed adsorber (zeolite13X-CMS3K)
(Cavenati et al., 2006)
Column Zeolite13X CMS3K
Height of adsorbent layer/column, m 0.6 0.2 0.4
Wall thickness of column, m 0.0024
Internal diameter of column, m 0.016
Density of column wall, kg/m3 8238
Inter-particle voidage/column porosity 0.33
Specific heat capacity, J/kg/K 500 920 880
Bulk density/ column density, kg/m3 756 715
Thermal conductivity of column wall, W/m/K 13.40
Particle/extrude density of zeolite13X 1130 1040
Particle/ extrude radius of zeolite13X, m 0.0008 0.0009
Intra-particle voidage/extrude porosity 0.54 0.46
Extrude tortuosity 2.2 2
Page 82
66
Table 4.5: Parameters used in simulation of zeolite13X-CMS3K system
Zeolite13X CMS3K
Total Pressure, bars 2.5, 5, 7.5, 10
Flow rate, SLPM 1.6
Temperature, K 300
Mass transfer coefficient, 1/s CH4 – 0.403 CH4 – 0.00004
CO2 – 0.018 CO2 – 0.0086
N2 – 0.112 N2 – 0.0047
Heat transfer coefficient, W/m2/K Gas-Solid – 60 Gas-Solid – 65
Gas-wall – 36 Gas-wall – 39
Wall-ambient – 192 Wall-ambient – 192
Isotherm parameters for CH4 a1 – 0.0112 a1 – 0.000171
a2 – 0.00029 a2 – 0.000172
a3 – 0.834 a3 – 0.716
a4 – 1590 a4 – 3190
a5 – 0.00037 a5 – 0.00001
a6 – 1610 a6 – 2980
Isotherm parameters for CO2 a1 – 0.00033 a1 – 0.00049
a2 – 0.0021 a2 – 0.0105
a3 – 0.43 a3 – 0.492
a4 – 2850 a4 – 2160
a5 – 0.0031 a5 – 0.00147
a6 – 2450 a6 – 2040
Isotherm parameters for N2 a1 – 0.0022 a1 – 0.000003
a2 – 0.00042 a2 – 0.871
a3 – 0.885 a3 – 0.796
a4 – 1740 a4 – 1460
a5 – 0.0001 a5 – 0.0011
a6 – 1970 a6 – 1360
Note: Transport coefficients were calculated (70%CH4/ 20%CO2/10% N2/2.5bars/300K).
Page 83
67
(a) 2.5 bars (b) 5.0 bars
(c) 7.5 bars (d) 10.0 bars
(Note: 75CH4-15N2-10CO2 means 75 mol % CH4, 15 mol % N2 and 10 mol CO2. Other
legends shall be read same way)
Figure 4.7: Total amount (kg/mol of feed gas) of adsorbents for N2 and CO2 separation
from natural gas for zeolite13X-CMS3K adsorber
0
10
20
30
40
50
60
70
80
90
100
0.00 1.00 2.00 3.00 4.00 5.00
N2
Sep
ara
tio
n e
ffic
ien
cy
(%
)
Total amount of adsorbent
(kg/mol of feed gas)
75CH4-15N2-10CO2
65CH4-15N2-20CO2
65CH4-25N2-10CO2
55CH4-25N2-20CO2
0
10
20
30
40
50
60
70
80
90
100
0.00 0.50 1.00 1.50 2.00
N2
Sep
ara
tio
n e
ffic
ien
cy
(%
)
Total amount of adsorbent
(kg/mol of feed gas)
75CH4-15N2-10CO2
65CH4-15N2-20CO2
65CH4-25N2-10CO2
55CH4-25N2-20CO2
0
10
20
30
40
50
60
70
80
90
100
0.00 0.50 1.00 1.50 2.00
N2
Sep
ara
tio
n e
ffic
ien
cy
(%
)
Total amount of adsorbent
(kg/mol of feed gas)
75CH4-15N2-10CO2
65CH4-15N2-20CO2
65CH4-25N2-10CO2
55CH4-25N2-20CO2
0
10
20
30
40
50
60
70
80
90
100
0.00 0.20 0.40 0.60 0.80 1.00 1.20
N2
Sep
ara
tio
n e
ffic
ien
cy
(%
)
Total amount of adsorbent
(kg/mol of feed gas)
75CH4-15N2-10CO2
65CH4-15N2-20CO2
65CH4-25N2-10CO2
55CH4-25N2-20CO2
Page 84
68
4.3.1 Parametric study
Parametric studies were performed to determine the effect of feed conditions on
adsorption of CO2 and N2. Three effects were determined. They are: (i) the effect of feed
pressure (ii) the effect of concentration and (iii) the effect of N2 separation efficiency.
Effect of feed pressure: Figure 4.8 plots nitrogen separation efficiency of a
double bed (zeolite13X-CMS3K) adsorption column against the total amount of
adsorbent at various pressures for two different feed compositions: (i) 75% CH4-15% N2-
10% CO2 and (ii) 55% CH4-25% N2-20% CO2. As being evident, feed pressure has
significant effects on the separation of CO2 and N2. High feed pressure requires less
adsorbent, while low feed pressure requires more adsorbent. Also, the effect of the
differential pressure increment, 2.5 bars in this study, on the amount of adsorbent for a
particular separation efficiency became reduced.
Figure 4.9 plots the effect of feed-gas pressure on the required amount of
adsorbent for three separation efficiencies (70%, 80%, and 90%). The distinct points,
when fitted, show power law relationships. As evident from this figure (4.9), a pressure
increase of 2.5 bars from 2.5 to 5 bars for 80% N2 separation is 1.18 kg/mol, for 5 to 7.5
bars, the amount is 0.4 kg/mol, and for 7.5 bars to 10 bars, the amount is 0.24 bar. These
reduced differential amounts also explain the saturation of adsorption capacity of
adsorbents at high pressure.
Page 85
69
(a) 75% CH4-15% N2-10% CO2
(b) 55% CH4-25% N2-20% CO2
Figure 4.8: Effect of feed pressure on N2 separation efficiency (%) for
zeolite13X-CMS3K system
0
10
20
30
40
50
60
70
80
90
100
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
N2
sep
ara
tion
eff
icie
ncy
(%
)
Total amount of adsorbent
(kg per mole of feed gas)
Feed gas pressure, 2.5 bar
Feed gas pressure, 5 bar
Feed gas pressure, 7.5 bar
Feed gas pressure, 10 bar
0
10
20
30
40
50
60
70
80
90
100
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
N2
sep
ara
tion
eff
icie
ncy
(%
)
Total amount of adsorbent
(kg per mole of feed gas)
Feed gas pressure, 2.5 bar
Feed gas pressure, 5 bar
Feed gas pressure, 7.5 bar
Feed gas pressure, 10 bar
Page 86
70
Note: Total amount denotes amount of zeolite13X and CMS3K.
Figure 4.9: Effect of feed-gas pressure on total amount of adsorbents for 70 to 90% N2
separation efficiency for zeolite13X-CMS3K system
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0.0 2.5 5.0 7.5 10.0
To
tal a
mo
un
t o
f a
dso
rb
en
t
(kg
per m
ole
of
feed
ga
s)
Feed gas pressure (bar)
70%
80%
90%
Page 87
71
Effect of feed composition: Presence of N2 and CO2 in various amounts may
affect the nitrogen separation efficiency of the double bed adsorber. Since all the CO2
was removed in zeolite13X, CO2 has no effect on the N2 separation efficiency of
CMS3K. However, zeolite13X also adsorbs some N2, and the amount of zeolite13X
needed for CO2 separation depends on the concentration of CO2 in the feed. Thus, the
effects of concentration of CO2 may not be significant on overall efficiency, but it will
have a positive effect on the N2 separation efficiency of CMS3K. Overall, the effect of N2
concentration on separation efficiency will be reduced. A further reduced effect was
expected as the double bed adsorber was operated in short cycle time to facilitate kinetic
separation.
Figure 4.10 shows the effect of feed composition on nitrogen separation
efficiency at 2.5 bars and 300K. Feed compositions did not show any significant effect on
the required amount of adsorbent for a specified nitrogen separation efficiency. This is
due to the short cycle time, which limits the ability of the mass or heat transfer parameter,
such as diffusion or conduction, to play a significant role. Nitrogen separation efficiency
was found to vary a maximum of 3.5% (AAD, average absolute deviation) at 2.5 bars.
Since the results of other feed pressures showed a similar trend, they are not shown here.
Figure 4.10a presents a comparison of the effect of the change in concentration of N2.
Here, the concentration of CO2 is constant, while the concentration of CH4 changes. The
efficiency loss, 3.5%, is due to presence of extra N2 in the feed. A similar result was
obtained for 20% CO2. Again, the loss in adsorption efficiency is due to extra N2 that
enters the column.
Page 88
72
(a) Fixed concentration of CO2
(b) Fixed concentration of N2
Figure 4.10: Effect of feed concentration on nitrogen separation efficiency at 2.5 bars for
zeolite13X-CMS3K system
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5
N2
sep
ara
tio
n e
ffic
ien
cy
(%
)
Total amount of adsorbent
(kg per mole of feed gas)
[email protected] @2.5bar
0
10
20
30
40
50
60
70
80
90
100
0 1 2 3 4 5
N2
sep
ara
tio
n e
ffic
ien
cy
(%
)
Total amount of adsorbent
(kg per mole of feed gas)
[email protected]
[email protected]
Page 89
73
Effect of N2 separation efficiency: Figure 4.11 plots the total amount of
adsorbent (kg per mole of feed gas) against the N2 separation efficiency of the
zeolite13X-CMS system. As is evident, the there is less of an effect at high feed pressure
(10 bars), while it is significant at low feed-gas pressure (2.5 bar). In these two plots, the
concentration of CO2 was kept constant (10 %), while concentrations of N2 were
changed: 25% N2 (Figure 4.11(a)) and 15% N2 (Figure 4.11(b)). In both cases, the trends
of effects are similar.
4.3.2 Correlations based on simulated results
The effects of feed pressure were correlated to give the amount of total adsorbent
needed for nitrogen separation. The correlation (4.2) shown below reproduces the amount
of total adsorbent at pressures of 2.5, 5, 7.5, and 10 bars with AADs of 3.36%, 4.23%,
3.75%, and 5.28 % for all feed compositions.
)()(54
)()(132
32
b
n
b
n
b
n
b
n
Pbb
PbQ
4.2
where Q is the total amount (kg per mole of feed gas) of adsorbent, Pn is the partial
pressure of N2, ηn is the separation efficiency (%), and b1 to b5 are constants (Table 4.6).
The results produced by the correlation were compared to simulated results. Figure 4.12
shows the comparison of the results for all pressures and for the feed composition of 75%
CH4, 15% N2, and 10 % CO2. The average absolute deviations observed for this feed
composition were 3.63%, 2.29%, 1.03%, and 3.71%.
Page 90
74
(a) 75% CH4-25% N2-10% CO2
(b) 55% CH4-15% N2-10% CO2
Figure 4.11: Effect of N2 separation efficiency on total amount of adsorbent for
zeolite13X-CMS3K system
0
1
2
3
4
5
0 20 40 60 80 100
To
tal a
mo
un
t o
f a
dso
rb
en
t
(kg
per m
ole
of
feed
ga
s)
N2 separation efficiency (%)
Feed gas pressure, 2.5 bar
Feed gas pressure, 5 bar
Feed gas pressure, 7.5 bar
Feed gas pressure, 10 bar
0
1
2
3
4
5
0 20 40 60 80 100
To
tal a
mo
un
t o
f a
dso
rb
en
t
(kg
per m
ole
of
feed
ga
s)
N2 separation efficiency (%)
Feed gas pressure, 2.5 bar
Feed gas pressure, 5 bar
Feed gas pressure, 7.5 bar
Feed gas pressure, 10 bar
Page 91
75
Table 4.6: Parameters for Correlation 4.2
parameter Feed Pressure (bars)
2.5 5.0 7.5 10.0
b1 0.362 0.410 0.401 0.189
b2 0.030 0.011 0.010 0.032
b3 0.625 0.499 0.263 1.040
b4 6.801 10.376 9.576 40.856
b5 -0.311 -0.880 -2.626 -0.176
Page 92
76
Note: Simulated means results obtained from Aspen Adsorption while
predicted means results obtained from empirical correlation.
Figure 4.12: Comparison of simulated result with the results obtained from correlation
4.2 for feed composition of 75% CH4, 15% N2 and 10 % CO2 for zeolite13X-CMS3K
system
0
1
2
3
4
0 1 2 3 4
Pred
icte
d (
kg
per m
ole
of
feed
ga
s)
Simulated (kg per mole of feed gas)
Feed gas pressure, 2.5 bar
Feed gas pressure, 5 bar
Feed gas pressure, 7.5 bar
Feed gas pressure, 10 bar
Page 93
77
4.4 Simulation results for zeolite13X-ACB system
A double bed adsorber consisting of zeolite13X-ACB was used to determine the
amount of adsorbent for complete separation of CO2 and for various N2 separation
efficiencies. The first bed carried zeolite13X, which selectively removed CO2, and the
second bed consisted of ACB, which removed N2. The zeolite13X bed was applied first
to remove all the CO2 from the feed. ACB was then set to remove N2 from remaining gas
mixture. Five pressure stages (2.5 bars, 5 bars, 10 bars, 20 bars, and 30 bars) were
studied using 5 to 25% N2, 5 to 25% CO2, and 70% CH4.
A sample of inputs is tabulated in Table 4.7 and Table 4.8. The parameters shown
in the tables were kept unchanged during simulation. Some other properties, such as mass
transfer coefficients, changed with concentration or pressure changes. The feed was
continued in 10 minutes cycles at a constant flow rate of 1.16 SLPM. This cycle time (10
minutes) was decided on by analyzing several breakthrough simulations with different
ratios of activated carbon to zeolite13X at 2.5 bars with a feed of 70% CH4, 20% CO2,
and 10% N2. The total amount of adsorbents needed for various levels of separation was
determined through simulation and is presented in Figure 4.13. According to Figure 4.13,
the highest amount of adsorbent (916 kg/kmol) was needed for 100% separation of CO2
and 95% of N2 from a feed stream of 70% CH4, 5% CO2, and 25% N2. Most of the
amount was activated carbon. The share of zeolite13X in this amount is only 4.35% (by
weight). Zeolite13X also adsorbed 2.92% of N2. The rest, 92.08 % nitrogen, was
adsorbed in activated carbon.
Page 94
78
Table 4.7: Physical properties of double bed adsorber (zeolite13X-ACB)
(Cavenati et al. (2006) and Shen et al. (2010))
Column Zeolite13X ACB
Height of adsorbent layer/column, m 0.6 0.2 0.4
Wall thickness of column, m 0.0024
Internal diameter of column, m 0.016
Density of column wall, kg/m3 8238
Inter-particle voidage/column porosity 0.33 0.32
Specific heat capacity, J/kg/K 500 920 650
Bulk density/column density, kg/m3 756 669
Thermal conductivity of column wall, W/m/K 13.40
Particle/extrude density of zeolite13X 1130 984
Particle/extrude radius of zeolite13X, m 0.0008 0.0006
Intra-particle voidage/extrude porosity 0.54 0.51
Tortuosity 2.2 2
Page 95
79
Table 4.8: Parameters used in simulation of zeolite13X-ACB system
Zeolite13X ACB
Total Pressure, bars 2.5, 5, 10, 20, 30
Flow rate, SLPM 1.6
Temperature, K 300
Mass transfer coefficient, 1/s CH4 – 0.403 CH4 – 0.1252
CO2 – 0.018 CO2 – 0.0963
N2 – 0.112 N2 – 0.7030
Heat transfer coefficient, W/m2/K Gas-Solid – 60 Gas-Solid – 62
Gas-wall – 36 Gas-wall – 39
Wall-ambient – 192 Wall-ambient – 192
Isotherm parameters for CH4 a1 – 0.0112 a1 – 0.00057
a2 – 0.00029 a2 – 0.00059
a3 – 0.834 a3 – 0.8419
a4 – 1590 a4 – 2484
a5 – 0.00037 a5 – 0.00005
a6 – 1610 a6 – 2663
Isotherm parameters for CO2 a1 – 0.00033 a1 – 0.00123
a2 – 0.0021 a2 – 0.00287
a3 – 0.43 a3 – 0.694
a4 – 2850 a4 – 1996
a5 – 0.0031 a5 – 0.00001
a6 – 2450 a6 – 2972
Isotherm parameters for N2 a1 – 0.0022 a1 – 0.0107
a2 – 0.00042 a2 – 0.00035
a3 – 0.885 a3 – 0.8491
a4 – 1740 a4 – 1362
a5 – 0.0001 a5 – 0.000001
a6 – 1970 a6 – 2486
Note: Transport coefficients were calculated (70%CH4/ 20%CO2/10% N2/2.5bars/300K).
Page 96
80
(a) 2.5 bars (b) 5 bars
(c) 10 bars (d) 20 bars
(e) 30 bars
0
10
20
30
40
50
60
70
80
90
100
0 200 400 600 800 1000
N2
sep
ara
tio
n e
ffic
ien
cy
(%)
Total amount of adsorbent
(g/mol of feed gas)
10% CO2 - 20% N2
15% CO2 - 15% N2
20% CO2 - 10% N2
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400 500
N2
sep
ara
tio
n e
ffic
ien
cy
(%)
Total amount of adsorbent
(g/mol of feed gas)
10% CO2 - 20% N2
15% CO2 - 15% N2
20% CO2 - 10% N2
0
10
20
30
40
50
60
70
80
90
100
0 50 100 150 200 250 300 350
N2
sep
ara
tio
n e
ffic
ien
cy
(%)
Total amount of adsorbent
(g/mol of feed gas)
10% CO2 - 20% N2
15% CO2 - 15% N2
20% CO2 - 10% N2
0
10
20
30
40
50
60
70
80
90
100
0 50 100 150 200
N2
sep
ara
tio
n e
ffic
ien
cy
(%)
Total amount of adsorbent
(g/mol of feed gas)
10% CO2 - 20% N2
15% CO2 - 15% N2
20% CO2 - 10% N2
0
10
20
30
40
50
60
70
80
90
100
0 50 100 150 200
N2
sep
ara
tio
n e
ffic
ien
cy
(%)
Total amount of adsorbent
(g/mol of feed gas)
10% CO2 - 20% N2
15% CO2 - 15% N2
20% CO2 - 10% N2
Figure 4.13: Total amount of
adsorbents for N2 separation at
different feed pressures and
compositions (zeolite13X-ACB
system)
Page 97
81
4.4.1 Parametric study
Parametric studies were performed to determine the effect of feed conditions on
the adsorption of CO2 and N2. Three effects were determined. They are: (i) the effect of
feed pressure (ii) the effect of concentration and (iii) the effect of N2 separation
efficiency.
Effect of feed pressure: Feed pressure has considerable impact on the required
amount of adsorbents. High feed pressure required a low amount of adsorbent, while a
high amount of adsorbent was needed for low pressure. Figure 4.14 shows the amount of
adsorbents required for different pressures for a feed stream of 70% CH4, 15% CO2, and
15% N2. A maximum of 783 g/mol of adsorbents were needed to separate 95% of N2 at
2.5 bars while the number for 30 bars is 156 g/mol. The amount is reduced by 627 g/mol
when pressure was changed to 2.5 bars from 30 bars. A similar trend was also found for
other feed composition and separation levels.
Page 98
82
Figure 4.14: Effect of feed pressure on total amount of adsorbent for different N2
separation efficiencies (zeolite13X-ACB system)
0
100
200
300
400
500
600
700
800
0 5 10 15 20 25 30
To
tal a
mo
un
t o
f a
dso
rb
en
t
(g/m
ol o
f fe
ed
ga
s)
Feed gas pressure (bar)
95% N2 separation
85% N2 separation
75% N2 separation
Page 99
83
Effect of feed composition: Figure 4.15 shows the total amount of adsorbent as
a function of concentration of CO2 and N2 at various feed pressures. The top plot of the
figure shows that the total amount of adsorbent decreases with an increasing
concentration of CO2, while the bottom plot shows an increase in adsorbent amount. The
conflict reveals that the amount of activated carbon for N2 removal is higher when
compared to zeolite13X for CO2 removal. This can be credited to the equilibrium
adsorption capacity of zeolite13X and ACB. Another notable point is the diminishing
nature of concentration effect at higher pressure. This indicates that the adsorption
capacity of adsorbents becomes limited after a certain pressure.
Effect of N2 separation efficiency: Figure 4.16 plots the total amount of required
adsorbents as a function of N2 separation efficiency. The plots were drawn for the lowest
feed-gas pressure (2.5 bars) and highest feed-gas pressure (30 bars) of this study. The
feed contained 25%, 15%, and 5% N2. The other two concentrations (10% N2 and 20%
N2) were dropped for clarity of the plots. As evident from the plots, the amount of
adsorbent is high for high separation efficiency. The relationship seems linear at low feed
pressure, while at high pressure, it is not. Also, the relationship changes for over 90%
separations. The starting point of separation efficiency refers to adsorbed amount of N2 in
zeolite13X.
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(a) Effect of concentration of CO2
(b) Effect of concentration of N2
Figure 4.15: Effect of concentration on total amount of adsorbents at different feed
pressures for zeolite13X-ACB system
0
100
200
300
400
500
600
700
800
900
1000
0 5 10 15 20 25
To
tal a
mo
un
t o
f a
dso
rb
en
ts
(g/m
ol o
f fe
ed
ga
s)
CO2 concentration (%)
Feed gas at 2.5 bar
Feed gas at 5 bar
Feed gas at 10 bar
Feed gas at 20 bar
Feed gas at 30 bar
0
100
200
300
400
500
600
700
800
900
1000
0 5 10 15 20 25 30
To
tal a
mo
un
t o
f a
dso
rb
en
ts
(g/m
ol o
f fe
ed
ga
s)
N2 concentration (%)
Feed gas at 2.5 bar
Feed gas at 5 bar
Feed gas at 10 bar
Feed gas at 20 bar
Feed gas at 30 bar
Page 101
85
(a) Feed gas pressure 2.5 bars
(b) Feed gas pressure, 30 bars
Figure 4.16: Effect of N2 separation efficiency on total amount of adsorbent for feed
pressures of (a) 2.5 bars and (b) 30 bars (zeolite13X-ACB system)
0
100
200
300
400
500
600
700
800
900
1000
0 10 20 30 40 50 60 70 80 90 100
To
tal a
mo
un
t o
f a
dso
rb
en
t
(g/m
ol o
f fe
ed
ga
s)
N2 separation efficiency (%)
25% N2
15% N2
5% N2
0
20
40
60
80
100
120
140
160
180
200
0 10 20 30 40 50 60 70 80 90 100
To
tal a
mo
un
t o
f a
dso
rb
en
t
(g/m
ol o
f fe
ed
ga
s)
N2 separation efficiency (%)
25% N2
15% N2
5% N2
Page 102
86
4.4.2 Correlations based on simulated results
The amounts of adsorbents determined from the feed pressures were correlated in
a single equation:
11105
7652
)1(98
)1()43(1ddd
dddd
yyPdd
yyPddSdQ
4.3
where w is the amount of adsorbent, S is the separation factor, P is the feed pressure, y is
the mole fraction of N2 or CO2, and d1 to d11 are parameters. The correlation determines
the total amount of adsorbents and the amount of zeolite13X depending on the input
parameters shown in Table 4.7. There are 2 sets of parameters listed in this table. They
entail the total amount of required adsorbent depending on the N2 content of the feed.
Figure 4.20 shows the amount of adsorbents obtained from simulation (points) and the
prediction of the correlation for the feed stream of 70% CH4, 25% CO2, and 05% N2. The
predicted results deviated from the simulated results by 3.8% (AAD). Maximum
deviation was observed for 85% nitrogen separation at 5 bars. The amount of adsorbent
under this condition was under the amount predicted by 4.6%. The predicted results for
the feed stream that carried 70% CH4, 05% CO2, and 25 % N2 showed an average
absolute deviation of 1.8%. Maximum absolute deviation was 5.5%.
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Table 4.9: Parameters for correlation 4.3
Parameter Nitrogen (mol/mol)
y<0.15 y≥0.15
d1 4.773 3.719
d2 1.026 1.032
d3 1.648 1.315
d4 0.413 0.241
d5 0.039 0.108
d6 0.042 0.070
d7 0.516 0.118
d8 32.542 84.280
d9 0.079 -1.411
d10 1.502 -1.182
d11 0.912 2.653
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Note: Simulated means results obtained from Aspen Adsorption while
predicted means results obtained from empirical correlation.
Figure 4.17: Comparison of simulated and predicted (correlation 4.3) results
0
200
400
600
800
1000
0 200 400 600 800 1000
Pred
icte
d a
mo
un
t (g
m/m
ol)
Simulated amount (gm/mol)
95% N2 separation
85% N2 separation
75% N2 separation
Page 105
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4.5 Determination of column dimensions using correlations
The procedure for the determination of column dimensions is described below. A
flow diagram, Figure 4.18, is, also, included.
Step1- Determination of amount of zeolite13X: Using correlation 4.1, the
required amount of zeolite13X for complete separation of CO2 can be determined. The
required inputs are feed pressure and concentration (mole fraction) of CO2. Parameters
for the correlation can be found in Table 4.3.
Step2 - Determination of total amount of adsorbent: The total amount of
adsorbent can be determined from correlations in Tables 4.2 or 4.3 for zeolite13X-
CMS3K and zeolite13X-ACB systems, respectively. The required inputs are feed
pressure, concentration of nitrogen, and separation efficiency (%) or separation factor for
zeolite13X-CMS3K and zeolite13X-ACB systems, respectively.
Step3 - Determination of amount of CMS3K and ACB: The amount of CMS3K
or ACB is the difference of the amounts obtained using correlations from Tables 4.2 and
4.1 or 4.3 and 4.1, respectively.
Step4 - Determination of volume of adsorbents: The total volume of adsorbents
is the sum of the volume of zeolite13X (determined at Step-1) and the volume of CMS3K
or ACB. The volume of individual adsorbents can be obtained by dividing the adsorbent
amount by its bulk density. Bulk density can be found in Tables 4.1, 4.4, or 4.7 for
zeolite13X, CMS3K, and ACB, respectively.
Step5 - Determination of dimensions of column: Flow velocity of the pipeline
can be converted into instantaneous velocity by using column porosity. The obtained
velocity is then lowered to accommodate retention time. This lowered velocity can be
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90
used to obtain the cross-sectional area of the column. Then, column length can be
determined by dividing the total volume of adsorbent by cross-sectional area of the
column.
Note: Diameter does not affect the performance of the column. The system can be used
for larger diameter.
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91
Figure 4.18: Calculation procedure for determination of column dimension using
correlations
Volume
Total Length
Porosity
zeolite13X
Prosity
CMS3K/ACB
Process conditions
Volume
CMS3K or ACB
Volume
Zeolite13X
Flow rate
Column
diameter
Column
CMS3K or ACB
Amount (g/mol)
Zeolite13X
Correlation 4.2 or 4.3
Total amount (g/mol)
Zeolite13X+CMS3K/ACB
Amount (g/mol)
Pressure
Concentration of CO2 and N2
Required N2 separation efficiency
Correlation 4.1
Pressure
Concentration of CO2
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5 Conclusions and Recommendations for future work
5.1 Conclusions
We developed a two-step design method for a layered bed adsorber for the
selective separation of CO2 and N2 from natural gas using zeolite13X, CMS3K, and
ACB. This two-step design method determines important design parameters and the
amount of adsorbents and then transforms the amount of adsorbents into physical
dimensions of the column. This method will be useful in designing practical separation
processes to produce pipeline grade NG.
Mathematical correlations, the first of their kind, were developed as a part of this
design process. These correlations determine the amount of adsorbents using information
such as feed pressure, concentration of CO2 and N2, and the extent of desired separation.
Moreover, these correlations show the way to derive preliminary designs at reduced cost
as they eliminate extensive simulation or experiments.
A step by step procedure was outlined for transforming the information obtained
by correlation into physical dimensions of the column. The procedure also offers a
flexible opening for gas velocity. Usual pipeline velocity can be used to obtain design
parameters. The flexibility in velocity will help the designer to keep control of column
dimensions such as diameter and length.
A parametric study was performed on a single-bed adsorption system to evaluate
(i) the contribution of each of the three mass transfer resistances present in the adsorption
separation process and (ii) the contribution of heat transfer modes. The study revealed
that (i) macropore resistance was dominant in zeolite13X, and (ii) convective heat
transfer was more pronounced than the conductive heat transfer in gas and adsorbent.
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A parametric study was performed on a layered bed (zeolite13X-CMS3K and
zeolite13X-ACB) adsorption system. One notable finding was the reduction of CO2
adsorption capacity of zeolite13X at high pressure (approximately 7.5 bars and over) in
the presence of N2. Another noteworthy observation was the reversal of selectivity of
CO2 over N2 on zeolite13X. In zeolite13X-CMS3K systems, the effects of N2 on
concentration were found to be insignificant, while zeolite13X-ACB systems showed
considerable effects.
Parameters of the isotherm model were obtained from the fitting of experimental
data. Several isotherm models were tried. The temperature dependency of those isotherm
models were also analyzed to account for temperature variations due to the heat of
adsorption. The temperature-dependent Langmuir-Freundlich model was found to be the
best fit.
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5.2 Recommendations for future work
In this work, multicomponent adsorption was implemented with the help of the
ideal adsorption solution theory in the absence of experimental data on multicomponent
adsorption. The theory uses pure component equilibrium information to calculate the
mixture properties. Experimental study of multicomponent gas mixture shall be done.
This will help to determine the optimum design pressure of a double bed adsorber.
Page 111
95
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Appendix – A: Adjustments of transport parameters
Effects of transport parameters were evaluated for the adsorption of CO2 in
zeolite13X and N2 in ACB and CMS3K. The determined effects helped to maintain a
simplified model without sacrificing the rigour of the model. As an example, highlights
of CO2-zeolite13X systems are described below. The effects were determined using a gas
flow rate 8.74E-07kmol/s (70%CH4, 20% CO2, and 10% N2) in a cylindrical layer of
zeolite (0.20m length x 0.016m diameter) at 2.5 bars and 300K, exactly the same as the
experimental setup previously reported (Cavenati et al., 2005).
Effect of mass transport parameters: The mass transfer analysis was based on the
breakthrough behavior of a fixed-bed adsorption column. The breakthrough curve was
produced using different mass transfer resistances. The resistances were also combined to
check their combined effect on the breakthrough curve. The objective was to identify an
effective mass transfer coefficient for every component of the gas mixture. Three forms
of mass transfer resistances were tested against observed dynamics of the fixed-bed
adsorption process (Figure 4.2). The macropore resistance was identified as a major
contributor for the natural gas-zeolte13X system based on predicted breakthrough
behaviour, i.e., the dynamics of the fixed-bed adsorption column. The observed
dynamics lead to the use of a resistance that is lower than the calculated macropore
resistance. This new value predicted the breakthrough behavior of the column with better
accuracy. It can be concluded that major mass transfer resistances in the zeolite bed exist
in the macropores, and the model takes on simplified forms as two other contributors
becomes less significant and, hence, the computation time will be reduced.
Page 123
107
(a) Effect of single mass transfer resistance
(b) Effect of combined mass transfer resistance
Figure A.1: Breakthrough of CO2 in zeolite13X for various mass transfer resistances
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0 400 800 1200 1600 2000
CO
2 (
mo
l/m
ol)
at
bed
ex
it
Time (second)
Cavenati et al., 2006
Film
macropore
micropore
0.00
0.01
0.02
0.03
0.04
0.05
250 300 350 400
CO
2(m
ol/
mo
l) a
t b
ed
ex
it
Time (second)
Cavenati et al., 2006
Film
macropore
micropore
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0 400 800 1200 1600 2000 2400
CO
2 (
mo
l/m
ol)
at
bed
ex
it
Time (second)
Cavenati et al.,
2006
Macropore
Film+
macropore
macropore+
micropore
Film +
macropore +
micropore
0
0.01
0.02
0.03
0.04
0.05
300 320 340 360 380 400
CO
2(m
ol/
mo
l) a
t b
ed
ex
it
Time (Second)
Cavenati et al.,
2006
Macropore
Film+
macropore
macropore+
micropore
Film +
macropore +
micropore
Page 124
108
Figure A.1(a) shows the individual effect of film, macropore, and micropore
resistances. When compared to the literature breakthrough point (340 seconds), it shows
an extended breakthrough point (370 seconds) for film and micropore resistance and a
short break through (330 seconds) for macropore resistance. This indicates that actual
resistances are larger than macropore resistance and, hence, a combination of resistances
may present in the system. Figure A.1(b) shows the effect of combined resistances.
Again, it is evident that macropore resistance is dominant, though it does not explain the
experimental breakthrough in full. Further investigation was carried out by changing the
bed porosity (Figure A.2). It was found that the bed porosity is related to the macropore
resistance by a factor of ε//(1-ε) rather than ε. Figure A.2 shows the breakthrough
comparison for this modified case. It is noticeable that this result gives better agreement
with literature. Since it is a single case study, we cannot generalize this finding at this
point. However, it certainly can be used in specific cases described in this study. This
modified resistance model was used to analyze the heat transfer issues associated with the
system.
Page 125
109
Figure A.2: Breakthrough of CO2 in zeolite13X with modified macropore resistance
0.00
0.04
0.08
0.12
0.16
0.20
0 400 800 1200 1600 2000
CO
2 (
mo
l/m
ol)
at
bed
ex
it
Time (Second)
Cavenati et al., 2006
Modified Macropore
resistance
Page 126
110
Effect of heat transport parameters: Adsorption is an exothermic process that
releases heat due to fluctuations in the surface energy of solid and thermal energy of
adsorbate molecules. This released heat is partly adsorbed by the solid and experiences a
rise in temperature, which slows down the kinetics and then the dissipation of heat to the
surroundings cools down the solid to facilitate additional adsorption. Hence, knowledge
of heat exchange is critical as it has an influence on local equilibrium and kinetics that
eventually straighten out the separation efficiency. Effects of heat transport parameters
were determined for the same system used for mass transport parameters, keeping mass
transport parameters as constant. It has been found that the convection heat transfer is
dominant in the system. The gas-solid heat transfer coefficient, i.e., the film heat transfer
coefficient depends on local conditions as the variable form of this coefficient diminishes
the temperature gaps between solid and gas phases. As expected, the solid phase and gas
phase conductivity were found to have negligible effects (Figure A.3). Wall conductivity
and external heat transfer are significant in determining shape of the dynamic profiles.
Page 127
111
(a) Breakthrough profile
(b) Temperature profile
Figure A.3: Effect of conductivity (gas and solid) on breakthrough dynamics
0.00
0.04
0.08
0.12
0.16
0.20
0 400 800 1200 1600 2000
CO
2(m
ol/
mo
l) a
t b
ed
ex
it
Time (second)
No conduction
gas+solid conduction
295
300
305
310
315
320
325
330
0 400 800 1200 1600 2000
Tem
pera
ture (
K)
at
bed
ex
it
Time (second)
No
Conduction
gas +
solid phase
conduction
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